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Copyright N°_ 



COPYRIGHT DEPOSIT. 



A LABORATORY MANUAL IN PHYSICS 



THE MACMILLAN COMPANY 

NEW YORK • BOSTON • CHICAGO • DALLAS 
ATLANTA • SAN FRANCISCO 

MACMILLAN & CO., Limited 

LONDON • BOMBAY • CALCUTTA 
MELBOURNE 

THE MACMILLAN CO. OF CANADA, Ltd, 

TORONTO 



A LABORATORY MANUAL 
IN PHYSICS 



TO ACCOMPANY 



BLACK AND DAVIS' "PRACTICAL PHYSICS 
FOR SECONDARY SCHOOLS" 



BY 
N. HENRY BLACK, A.M. 

SCIENCE MASTER, EOXBURY LATIN SCHOOL 
BOSTON, MASS. 



Neto fgotfe 

THE MACMILLAN COMPANY 

1913 

All rights reserved 






COPYBIGHT, 1913, 

By THE MACMILLAN COMPANY. 
Set up and electrotyped. Published September, 1913. 



Norruooti Stress 

J. S. Cushing Co. —Berwick & Smith Co. 

Norwood, Mass., U.S.A. 



©CI.A354.277 



INTRODUCTION 

It is now more than twenty years since we began to teach 
elementary physics in the laboratory and we already have 
many laboratory manuals. Why add another to the list? 
Every teacher of physics undoubtedly takes up the task of 
organizing his laboratory with great enthusiasm and high 
hopes. But sooner or later he finds that this business of 
teaching young people physics by means of laboratory exer- 
cises is a very difficult problem. No amount of costly appa- 
ratus or elaborate laboratory directions will produce that 
mental activity about physical phenomena that we all want 
to stimulate in our students. 

Doubtless the ideal method would be for each teacher to 
make his own laboratory manual, and many have done so. 
This book is the result of one teacher's attempt to get to- 
gether a set of experiments that represent a well-balanced 
course. The aim has been to make the directions so clear 
and concise that the average boy or girl, who already has in 
mind a general outline of the problem, can not only do the 
experiment but can also see the point to it. It is assumed 
that when the class assembles for the laboratory exercise 
the teacher will first make a few introductory remarks to 
indicate just what the problem of the day is and how it 
is related to the previous work and to the practical affairs 
of life ; then he will briefly outline just how the problem is 
to be attacked in the laboratory. If the student has already 
mastered the written directions, he ought then to be able 
to proceed intelligently and expeditiously with the work in 
hand. 



vi INTRODUCTION 

One reason why so much of our laboratory work in ele- 
mentary physics is ineffective seems to be that the students 
get lost in the multitude of details and forget the point or 
purpose of the experiment. Sometimes the directions are 
given with such minuteness that the work is purely me- 
chanical. This is reflected in the notebooks, which show 
no individuality and seem to indicate that the work has 
consisted merely in filling in certain blank spaces in a 
tabular form. It is, of course, expected that at first the 
student will need much help in arranging his notes in an 
orderly way, but these suggestions should be made less and 
less necessary as time goes on. The great danger in note- 
book work is artificiality. The student should write down 
in his own words such notes that when he reviews his work 
six months or a year later they will recall to his mind just 
what he did and what were his results. 

In the early days of student laboratory work a very large 
fraction of the time devoted to physics was spent in the lab- 
oratory, but in recent years we have come to believe that 
most subjects can be presented in their qualitative aspects 
best by the teacher in clean-cut lecture-table demonstrations, 
while the work of the student in the laboratory should be to 
perform a few well-selected experiments involving simple 
measurements. It is, of course, always to be remembered 
that this elementary work is not primarily physical meas- 
urements, but physics. Therefore it is hardly worth while 
at this stage of the work to spend much time in discussing 
percentage errors which are to be reckoned in tenths of one 
per cent. The engineer often has to be satisfied with results 
which check within 5%. Why should we seek for such a 
high degree of accuracy as can only be attained by compli- 
cating the apparatus and the manipulation? 

So it has come about that the suggested apparatus is very 



INTRODUCTION Vll 

simple and often crude. It is also suggested that the stu- 
dent do on an average only about one experiment per week. 
Frequent quizzes and reviews of the laboratory work have 
been found of great value. In this connection it is urged 
that the colleges provide for a practical laboratory exam- 
ination as a part of the admission examination in physics, 
and that the schools use such practical examinations as 
a part of the routine work to test the student's achieve- 
ments in physics. This laboratory examination should not 
be simply a repetition of experiments already performed, 
but should also to some extent test the student's originality 
and power to apply the methods of the laboratory to new 
problems. 

In his search for the best experiments, each teacher gath- 
ers ideas from so many sources that he hardly knows to 
whom he is indebted for the result. In this case, the author 
owes a great deal to his fellow members of the Eastern Asso- 
ciation of Physics Teachers, whose meetings have been so 
fruitful and suggestive. American teachers of elementary 
laboratory physics are under great obligations to Professor 
E. H. Hall of Harvard University for his persistent pioneer 
work in this field, and the author is under special obligations 
to him as his teacher, adviser, and friend. Professor J. M. 
Jameson of Pratt Institute has given a practical or engineer- 
ing aspect to several of the experiments (Nos. 17, 32, and 33) 
in mechanics and electricity. Finally, it is a great pleas- 
ure to acknowledge the help of Professor Hermann Hahn 
of Berlin, Germany, whose " Handbuch fur Physikalische 
Schuleriibungen " is a mine of suggestions and information 
about laboratory experiments in physicSo 

N. H. B. 



CONTENTS 



EXPERIMENT PAGE 

1. Measurement of a Eight Triangle and a Circle ... 1 

2. Density of a Block of Wood ....... 4 

3. The Straight Lever . 7 

4. The Weight of a Lever and its Center of Gravity . . 9 

5. Parallel Forces . . . . . . . . . . 11 

6. Inclined Plane ....... - . . . 13 

7. Sliding Friction 15 

8. Efficiency of a Commercial Block and Tackle 16 

9. Principle of Archimedes ........ 18 

10. Specific Gravity of a Solid ....... 20 

11. Specific Gravity of a Solid Lighter than Water . . 21 

12. Specific Gravity of a Liquid . . . . . .23 

13. Boyle's Law 25 

14. Density of Air .......... 27 

15. Specific Gravity of a Liquid by Balancing Columns . . 29 

16. Parallelogram of Forces ........ 31 

17. Forces acting on a Simple Truss 33 

18. Breaking Strength of Wire ....... 35 

19. Bending of Rods 37 

20. Accelerated Motion ......... 40 

21. The Fixed Points of a Thermometer ..... 42 

22. Linear Expansion of a Solid 44 

23. Cubical Expansion of Air ........ 47 

24. Specific Heat of a Metal 48 

25. Cooling Curve through the Melting Point . . . .51 

26. Latent Heat of Melting Ice ....... 52 

27. Latent Heat of Steam ........ 53 

28. Lines of Magnetic Force 55 

ix 



X CONTENTS 

EXPERIMENT PAGE 

29. The Voltaic Cell 57 

30. Magnetic Effect of a Current .60 

31. Electromotive Eorce 63 

32. The Fall of Potential along a Conductor 6Q 

33. Determination of Kesistance by Ammeter and Voltmeter . 68 

34. Measurement of Eesistance by Wheatstone Bridge . . 70 

35. Internal Resistance of a Battery .73 

36. Measurement of Current by a Copper Coulombmeter . . 75 

37. Induced Currents 77 

38. Efficiency of an Electric Motor 79 

39. Heating Effect of an Electric Current .... 82 

40. Frequency of a Tuning Fork .84 

41. Waye-Length of Sound 86 

42. Bunsen Photometer 88 

43. Image in a Plane Mirror . .90 

44. Images in Cylindrical Mirrors 92 

45. Index of Refraction of Glass ....... 95 

46. Focal Length and Conjugate Foci of a Converging Lens . 97 

47. Size and Shape of a Real Image ...... 99 

48. Magnifying Power of a Simple Lens ..... 102 

49. Telescope and Compound Microscope . 104 

50. Dispersion of Light by a Prism 106 

APPENDIX 109 



A LABORATORY MANUAL IN PHYSICS 



EXPERIMENT 1 



MEASUREMENT OF A RIGHT TRIANGLE AND A CIRCLE 

What is the relation betiveen the sides of a right triangle and 
also between the circumference and diameter of a circle? 



Sheet of paper. 
30 cm. rule. 
Right triangle. 



Cylinder or brass weight. 
Strip of thin paper. 
Pin. 



1. Right Triangle. Draw with a sharp hard lead pencil a 
right triangle with no two of its sides equal and none less 
than 10 cm. Make the corners clean and sharp. 
Label the triangle (Fig. 1) ABC, where is 
the right angle. Measure each of the three 
sides and record each length in centimeters 
and a decimal fraction of a centimeter. The 
millimeters are to be expressed as tenths of a 
centimeter (0.1 cm.), and the tenths of milli- 
meters, which are to be estimated, are to be expressed as 
hundredths of a centimeter (0.01 cm.). 

Record the measurements as follows : 




Fig. 1 



Sides 


Lengths 


AB 
BC 
AC 


. cm. 

. cm. 



To check these measurements, make the following compu- 
tation : (AB^ 2 = ■■• 

(BC) 2 = ... 

(Acy= ••• 

(Aoy+(Bcy = ... 

Compare (AB} 2 and (AC) 2 + (BC) 2 . 



2 LABORATORY MANUAL 

From a well-known proposition in Geometry, we know 
that in any right triangle the square of the hypothenuse is equal 
to the sum of the squares on the sides. 

So if the arithmetical computation has been done correctly, 
the difference between (AB) 2 and (AC) 2 + (BCy must be 
due to the errors in measurement. Since the measurement 
of each side is bound to be in doubt as to the hundredths 
of a centimeter (0.01 cm.), the square of each side can have 
no more than four significant * figures, and no more should be 
recorded. 

2. Circle. Measure the diameter across the circular face 
of a cylinder. Wrap tightly around the cylinder a thin 
strip of paper and prick a hole with a pin through the paper 
where it overlaps. Measure the distance between these pin- 
holes and record thus : 

Circumference = . cm. 

Diameter = . cm. 



Compute the value of 

circumference 



(By experiment.) 



diameter 

True value of ir = 3.14 (By Geometry.) 

Error = . . . . 

*Note. Since in each of the above measurements the tenths of a milli- 
meter had to be estimated, it follows that each measurement is uncertain to 
at least 0.01 cm. Eor example, suppose one side of the triangle measured 
12.46 cm. ; it would mean that we were certain of the first three digits 12.4, 
but that the 6 was doubtful and probably somewhat in error. 

Then it obviously follows that the square of 12.46 will also be somewhat 
in error. Let us see how much. 12 .- 

12.46 



7476 

4984 
2492 
1246 
155.2516 



MEASUREMENT OF A BIGHT TRIANGLE AND CIRCLE 3 

Problems. (1) A room is 3.55 meters high, 7.00 meters 
long, and 4.50 meters wide. Find the length of its diagonal 
to three significant figures. 

(2) A cow is fastened to a stake by a rope 20 feet long. 
Find the perimeter of the circle she can graze over, expressed 
in feet and inches. 



In the above computation, the doubtful digits are printed in black, and 
it will be seen that in the product we would retain only 155.3, saving only 
- one doubtful figure. The last figure saved would be written 3 instead of 2, 
because what was thrown away was more than one-half. 

As a general rule, in multiplying two numbers together, retain in the 
product only as many significant figures as there are in the least accurate 
factor. 

In the same way, when we divide two numbers, which are obtained from 
measurements and so are more or less inaccurate, we keep in the result 
only one doubtful figure. Thus, suppose the diameter of a circle measured 
5.25 cm. and the circumference 16.45 cm., then the quotient 3.13 has only 
three significant figures and the last 3 is somewhat uncertain. 

5.25 | 16.45 1 3. 13 
15 75 
700 
525 
1750 
1575 
175 

In general, then, all numbers obtained from measurement are more or less 
inaccurate, and we may retain as significant digits only one doubtful digit. 
The result of an arithmetical computation can never be more accurate than 
its least accurate factor. 



4 LABORATORY MANUAL 

EXPERIMENT 2 

DENSITY OF A BLOCK OF WOOD 

How many grams does one cubic centimeter of wood weigh ? 

Rectangular blocks, such as maple, Platform balance. 

oak, pine, mahogany. Set of weights. 

30 cm. rule. 

To get the density of wood, i.e. the weight per unit 
volume, it is necessary to get the weight and the volume of 
a sample block. 

First adjust the balance so that it will just balance evenly 
with no load in either scale pan. Then place the block of 
wood on the pan at the zero (left) end of the scale beam and 
counterbalance with weights. Steady the scale pans with 
the left hand while adding or removing the larger weights 
and so avoid jarring the balance and dulling the knife-edges. 
It will save time to begin by selecting a weight which is prob- 
ably a bit too heavy, and if so, take it off and replace it with 
the next smaller weight. Continue in this way until you 
have the largest weight which is lighter than the object. 
Add then the next smaller weight to the scale pan and so 
on until within 10 grams of the weight. To make the final 
adjustment use the slider. Take great care in counting up 
the weights used, and record this at once in the notebook 
as the weight of the block. 

The block of wood, although nearly rectangular, is not 
geometrically perfect, and therefore it is well to make several 
measurements of the length, width, and thickness. Then 
compute the average or mean length, width, and thickness, 
and so from these values the volume of the block. Finally, 
knowing the weight in grams of a certain number of cubic 



DENSITY OF A BLOCK OF WOOD 



centimeters of wood, we can easily compute the weight of one 
cubic centimeter, i.e. the density of the wood. 

To measure the block to 0.01 cm. with an ordinary meter 
stick, requires, however, considerable care. The block should 
be laid on a sheet of white paper in good light and the meas- 
uring stick should be placed upon 
it so that one end of the block is 
exactly in line with some centimeter 
mark, such as the 10 cm. mark, as 
shown in Fig. 2. The other end 
of the block will probably not lie 
exactly in line w T ith any millimeter 
mark on the scale and so it is necessary to estimate the frac- 
tion of millimeter. Express the result as centimeters and as 
a decimal fraction thereof, for example, 12.35 cm. To get 
d the length, measure each of the 



k 



^^^?^^5^P^5555555^^^^^ 



Fig. 2 




Fig. 



four edges parallel to the grain of 
the wood, a, 5, <?, and d in Fig. 3. 
It is not at all likely that each of 
these measurements, if carefully 
made, will give exactly the same 
result to 0.01 cm. In finding the average of four such meas- 
urements, it is customary to retain but one doubtful figure and 
if the second doubtful figure be 5 or more, then add one to 
the first doubtful figure. Thus : 

Length 

12.35 cm. 

12.37 cm. 
12.33 cm. 

12.38 cm. 



a. 
b. 
c. 
d. 



4 )49.43 cm . 
12.357 cm. 



Average Length 12.36 cm. 

To get the average width, measure each of the four long 
edges cross-wise the grain, e,f g, and h. In a similar man- 



6 



LABORATORY MANUAL 



ner measure the length of each of the four short edges, i,y, 
k, and ra, and call the average of these four measurements 
the thickness of the block. 

In computing the volume of the block, time will be saved 
if only significant figures are retained, that is, if only the 
first doubtful figure is kept. It should also be remembered 
that the result can be no more accurate than its least accurate 
factor, which is here the shortest side. 

It is very desirable to record all measurements and results 
in an orderly way and so the following is suggested : 

Weight of block No. = . . . . g. 

Length Width Thickness 

a , ___. cm . e. cm. t. - - cm. 

&. cm. /. cm. j. - cm. 

Ct -____-- cm. g. ------- cm. k. ------- cm. 

d. ------- cm. h. ------- cm. m. ------- cm. 

4) 4 ) 4 ) 

Average cm. Average cm. Average - - - - cm. 

Volume of block cm. 3 

Density of wood g./cm. 3 

Problem. If the density of aluminum is 2.6 g./cm. 3 , how 
many grams does an aluminum rod 20.0 cm. long and 1.00 
cm. in diameter weigh ? 



THE STRAIGHT LEVEE 



EXPERIMENT 3 

THE STRAIGHT LEVER 

How must the weights on a straight lever be arranged in order 

to balance? 

Meter stick. Set of weights. 

Fulcrum or support for meter stick. Thread. 

Suspend or support a meter stick at its mid-point, and if 
it does not quite balance, place on the lighter side a piece of 
bent copper wire at such a point as to produce equilibrium. 
Hang a 200-gram weight at a distance of 20 centimeters to 
the right of the fulcrum, and then hang a 100-gram weight 
at some point on the other side so as to produce equilibrium. 
Record these weights as W 1 and W 2 and their distances 
from the fulcrum as d x and d 2 (Fig. 4). 



I I I 1 II II I I I I I I I I : I I I I I I I II 

8 9 J 

I M I I I I I I I I I I I I ' I ' I ' I M I LI I 



w 2 



Fig. 4 






The turning effect or moment of a weight depends on the 
amount of the weight and its distance from the fulcrum. Thus 

Moment = weight x distance. 

Calculate the moment of each of these weights about the 
fulcrum (.F). 

Repeat, using a different set of weights and calculate the 
moment of each weight about the fulcrum. Compare these 
two products. 



8 LABORATORY MANUAL 

Then hang two weights at different points on the same 
side of the fulcrum and balance them with a single weight 
on the other side. Compute the sum of the moments on one 
side of the fulcrum and compare this sum with the moment 
on the other side. 

Finally suspend any convenient object, like a jackknife, 
screw driver, or monkey wrench, whose weight is not known, 
on one side of the lever and balance it with a known weight 
on the other side. Compute the weight of the object by the 
principle of moments which has just been illustrated. To check 
this result, weigh the object on the ordinary scales and com- 
pare the results. 

Arrange these data and results in some convenient tabular 
form. 

(a) What relation seems to exist between the moment of the 
weight on the right and that on the left of the fulcrum ? 

(6) How' does the sum of the moments on the right of the 
fulcrum compare with the sum of those on the left ? 

(c) Why does the weight of an object obtained by the meter- 
stick lever not agree exactly with that got on the scales ? 

Problem. A seesaw plank is set in an east and west 
direction. A boy weighing 100 lb. is placed 6 ft. west of 
the fulcrum ; a girl weighing 60 lb. is placed 6 ft. east of the 
fulcrum. Where must a second girl weighing 80 lb. be 
placed to balance the plank ? 



WEIGHT OF A LEVER AND ITS CENTER OF GRAVITY 9 

EXPERIMENT 4 

WEIGHT OF A LEVER AND ITS CENTER OF GRAVITY 

Wliere may the iveight of a lever be considered to act ? 

Meter stick loaded at one end. Set of weights. 
Triangular block of wood. Thread. 

The loaded meter stick AL. (Fig. 5) may be considered 
an example of a non-uniform lever whose weight cannot be 
neglected. Hang a known l x f b a 

weight W at some fixed ^^ A i 

point B, and then slide the ^^ ^ w 

meter stick along the tri- IG ' 

angular block of Avood until the whole thing just balances. 
Call the fulcrum F, and note AF, the distance of the fulcrum 
from the end of the meter stick. The distance BF is the 
lever arm of the weight W, and the moment of W about F is 
equal to W x BF. 

It is evident that part of the weight of the lever tends to 
turn the lever down on the right side and that the rest of 
the weight of the lever tends to turn it down on the left side. 
It would often be very convenient, in dealing with actual 
levers, if we could find a point where we could consider the 
whole weight as concentrated, that is, as if the lever weighed 
nothing and as if we had another weight applied at this 
point. Let us call such a point, if there be one, JT, and its 
distance from the fulcrum FX; then its moment is equal to 
the iveight of the lever times FX. But this moment is equal 
to the moment on the other side W x BF. In other words 
we have m ^ ^ x FX = w x BF ^ 

Wx BF 



and therefore FX = 



Wi. of lever 



10 



LABORATORY MANUAL 



Weigh the loaded meter stick and compute the value FX 
and so the position of Jon the meter stick, i.e. the distance 
AX. 

Repeat this experiment several times, using different 
known weights and at various positions, but each time com- 
puting AX. 

Compare the various positions of X and of the center of 
gravity (<76r) of the lever, which is found by balancing the 
lever alone without W. 

What does this experiment show about where the weight of a 
lever may be considered to act ? 

It will be well to arrange the results in some such way as 
the following : 

Weight of the loaded lever g. 



AB 



AF 



BF 



BFX W 



FX= 



BFXW 



Wt. of Lever 



AX 



100 g. 
200 g. 
200 g. 
500 g. 



10.0 cm. 
10.0 cm. 
15.0 cm. 



Center of gravity (CG) is located cm. from A. 



Problem. A boy who weighs 60 lb. uses as a seesaw a 
15-ft. plank which weighs 70 lb. and which has its center of 
gravity in the middle. If he sits 1 ft. from one end, how 
far from this same end must the fulcrum be placed in order 
to balance ? 



PARALLEL FORCES 



11 



EXPERIMENT 5 

PARALLEL FORCES 

What two conditions must always exist in order to have parallel 
forces in equilibrium ? 



4 spring balances (2000 g.). 
4 table clamps. 



Meter stick. 

Stout cord (fishline). 



Arrange the apparatus flat on the table as shown in the 
diagram (Fig. 6). Attach cords to the meter stick at vari- 




Fig. 6 



ous points, fasten the spring balances to these cords, and 
arrange the table clamps so that the meter stick is about 
parallel to the edge of the table and so that all forces are 
parallel. 



12 LABORATORY MANUAL 

Tighten the cords attached to F 2 and F s until the balances 
indicate 1000 g. and 1500 g. respectively, and adjust F 1 and 
F± until the whole is in equilibrium. Then read and record 
the readings of F v F v _F 3 , and F± and the distances AB, AC, 
AD, and AF. 

Repeat, using different values for F s and JF 4 , and finally re- 
peat with different positions for C and D. 

Compute in each case the sum of _F 2 and F s , and the sum 
of F 1 and F r 

Compute the moment of each force about A and find in 
each case the sum of the moments tending to produce clock- 
wise rotation and the sum of the moments tending to produce 
counterclockwise rotation. 

Compute the moments in one case about F as a turning 
point. Compare the sum tending to produce clockwise rota- 
tion with the sum tending to produce counterclockwise 
rotation. 

When several parallel forces are in equilibrium, (a) how 
does the sum of the forces in one direction compare with the sum 
of those in the opposite direction ; (b) how does the sum of the 
moments of the forces tending to produce clockwise rotation com- 
pare with the sum of the moments of the forces tending to pro- 
duce counter clockwise rotation? 

Problem. If forces of 6 lb. north, 8 lb. south, 10 lb. north, 
and 15 lb. south are applied at distances 4, 8, 12, and 16 ft. 
respectively from the western end of the rod, what force must 
be applied to produce equilibrium and at what point and in 
what direction must it be applied ? 



INCLINED PLANE 



13 



EXPERIMENT 6 



INCLINED PLANE 



How does the effort required to pull a loaded car up an in- 
clined plane depend on the grade ? 



Smooth board. 
Support for one end. 
Hall's car. 



Spring balance. 
Set of weights. 
Meter stick. 



Tip the board up at some convenient angle, such as 30°, 
and pull the car (TT), which has been previously weighed, 
slowly up the incline (Fig. 7). The effort required to do 




Fig. 7 

this is a little more than would be required if friction could 
be entirely eliminated. But if the car is allowed slowly to 
roll down the incline, the effort required to hold it back will 
be slightly less because of the friction. Therefore take the 
mean or average of these two pulls, as the force (JP) or effort 
which applied parallel to the incline would be needed to hold 
the car if there were no friction. 

The grade of an incline is the ratio of the height to the 
length. For example, a 15 % grade means an incline which 



14 



LABORATORY MANUAL 



rises 15 feet in going along the incline 100 feet. To compute 
the grade, then, measure some convenient height (JET) and 
its corresponding length (i) along the incline. If, for 
example, we measure from the table top to the upper side of 
the inclined board, then we must also measure along the 
upper side of the board to the point where this surface cuts 
the table, and so it is usually more convenient to use the 
lower side of the inclined board in measuring loth height and 
length. 

Repeat this experiment with different loads in the car, and 
with the inclined plane at different grades in order to find 
some relation between the effort (^), the total weight (W) 

XT TT 

(i.e. car + load), and the grade. Compare —-and — • 

W L 
Tabulate your data and results somewhat as follows: 





w 


F 


H 


L 


H 
L 


F 

W 









































Problem. What drawbar pull is necessary to pull a train 
weighing 350 tons up a grade of 15 ft. rise per mile of track, 
neglecting friction? 



SLIDING FRICTION 15 

EXPERIMENT 7 

SLIDING FRICTION 

How does starting friction compare with sliding friction ? How 
does sliding friction vary with pressure ? 

Friction board. Set of weights. 

Block of wood or friction box. Spring balance. 

The force needed to cause sliding varies much according 
to the materials, the condition of the bearing surface, lubrica- 
tion, etc. 

Place the board on the table and set the friction block or 
box upon it. Attach the spring balance to the block by a 
foot or two of cord (Fig. 8). By loading the. block with 
weights we may get ,p 

any desired pressure f^ 

between the bearing ^— <. ^= >- o I I 

surfaces. We may 



well start with as FlG - 8 

low a pressure as will give a fairly steady reading on the 
spring balance, and note carefully the force needed to start 
the loaded block and also the force required to keep it mov- 
ing slowly at a uniform rate. Then increase the load and 
measure in the same way the friction at five or six other 
pressures. 

The ratio between the force (_F) required to cause sliding, 
and the perpendicular pressure (P) between the bearing sur- 
faces, is called the coefficient of friction. Compute the coefficient 
of friction in each case as a decimal fraction. 

Record the results in tabular form : 



16 



LABORATORY MANUAL 



Trials 


I 


II 


in 


IV 


V 


VI 


Weight of block 

Load 

Weight of block and load, i.e. 
pressure ........ 

Starting friction 

Sliding friction 

Coefficient of friction .... 















How does the starting friction compare with the sliding friction ? 
Does the sliding friction increase with the pressure ? 
Does the coefficient of friction increase with the pressure ? 

Problem. If the coefficient of friction between two well- 
lubricated metal surfaces is 0.03, what force is needed to 
make 500 pounds slide ? 

EXPERIMENT 8 



EFFICIENCY OF A COMMERCIAL BLOCK AND TACKLE 

What fraction of the work put into a commercial block and 
taxkle is got out under various conditions ? 



Two double pulleys 

(commercial). 
Rope. 



Weights. 
Spring balance. 
Meter stick. 



Attach one block to a ring in the ceiling or to a suitable 
support from the wall, and apply various loads, such as 5, 
10, 15, 20 lb., to the movable pulley and determine — using 
the spring balance (Fig. 9) — the effort (F) required to 
raise the load (IT) slowly. Determine also the distance 
through which the effort must be exerted in order to lift the 



EFFICIENCY OF COMMERCIAL BLOCK AND TACKLE 17 



weight 1 foot. Compare this distance with that 
which you would expect from the arrangement 
of ropes and pulleys. 

Compute the input and output at the different 
loads for a hoist of 10 feet. The work " put in " 
is equal to the effort x effort distance, and the 
work " put out " of a machine is equal to resist- 
ance x resistance distance. Note that the out- 
put here means only the useful output, i.e. work 
done in lifting the load exclusive of the weight 
of the movable block. 

Finally compute the efficiency, i.e. ratio of out- 
put to input, of the commercial block and tackle 
at the different loads. Why is the efficiency not 
the same at different loads? What becomes of 
the "wasted ivork" ? 

Plot a curve to show graphically the relation 
between efficiency (vertical distance to curve) 
and load (horizontal distance). Explain the 
form of the curve. 

It will be convenient to record the data and 
results of this experiment in tabular form, some- 
what as follows : 



\W 



Fig. 9 



Effort moves through .... ft. when weight is lifted 10 ft. 



Loads 
(lb.) 



Effort 
(lb.) 



Output per 10 ft. Lift 

(ft. -lb.) 



Input 

(ft. -lb.) 



Efficiency = 
(%) 



Output 
Input 



18 



LABORATORY MANUAL 



Problem. If the maximum pull which three men can exert 
is 400 lb., and if a 1000-lb. piano is to be lifted by a block and 
tackle whose efficiency is assumed to be 65%, what is the 
least number of sheaves which can be used in each block? 
Draw a diagram. 

EXPERIMENT 9 



PRINCIPLE OF ARCHIMEDES 

I. Sow much does a body seem to lose in weight when en- 
tirely immersed in a liquid ? 

II. Sow much liquid does a floating body displace? 



Overflow can. 

Platform balance with weights and 

support, or spring balance. 
Solids (denser than water), 100-250 g., 

such as stone, coal, glass, etc. 



Solids (less dense than water) 
such as blocks of wood, 
apples, etc. 

Beaker or tumbler. 

Battery jar. 

Thread. 



I. Solids that Sink. By weighing a solid, such as a 
piece of stone, in air and then when entirely immersed in 
water, the loss in apparent weight can be computed. This 
loss of weight evidently depends on the size of the stone and 

so on the weight of the 
liquid displaced. 

To determine this weight 
of the liquid displaced, a 
can with a spout, called an 
overflow can (Fig. 10), is 
filled until water runs out 
of the spout. Then by plac- 
ing a weighed glass beaker 
under the spout and care- 




Fig. 10 



PRINCIPLE OF ARCHIMEDES 



19 



g- 

g- 

_gl 

g- 



fully lowering the piece of rock into the overflow can, the 
water which is displaced overflows into the beaker and may 
be caught and weighed. 

Record these observations and results as follows 

Weight of solid in air 

Weight of solid in water 

Loss of weight of solid in water 
Weight of catch glass, empty .... 
Weight of catch glass and water displaced 

Weight of water displaced . . . 

Compare the weight of the displaced water with the loss of 
weight of the stone in water. 

II. Solids that Float. To find 
out how the weight of a floating 
body compares with the weight of 
liquid displaced by it, first weigh 
the object, such as an apple or 
block of wood, and then arrange 
the overflow can and beaker as in 
Fig. 11, and determine the weight 
of water displaced by the floating object. 

The observations to be obtained are as follows : 

Weight of solid 

Weight of catch glass, empty .... 
Weight of catch glass and water displaced 
Weight of water displaced . . . 

Compare the weight of a floating object with the weight of the 
liquid displaced by it. 

Problem. A metal bar, 10 cm. long, 2 cm. wide and 
1.5 cm. thick, weighs 200 g. in water. How much does it 
weigh out of water ? 




Fig. 11 



g- 
g- 



20 



LABORATORY MANUAL 



EXPERIMENT 10 

SPECIFIC GRAVITY OF A SOLID 

How many times as heavy as an equal volume of water is a 
solid which sinks in water ? 



Solids (such as porcelain, solid 
glass stopper, pieces of metal, 
stones, sulphur, etc.), weigh- 
ing 100-250 g. 



Thread. 

Platform balance with weights 
and support, or spring balance. 
Battery jar. 



To get the weight of a piece of porcelain, glass, or metal, 
we have merely to weigh it in the usual way. To get the 
weight of an equal bulk of water, we make use of Archime- 
des' principle; namely, that the weight of an equal bulk of water 
is equal to the loss of weight when immersed in water. The 
specific gravity of a solid is the ratio of the weight of the solid 
to that of an equal volume of water. 

Record the observations and results in tabular form : 





G LASS 


Marble 




Weight of solid in air 

Weight of solid in water -* . 








Loss of weight in water . . . . . . 

Weight of equal volume water .... 

Specific gravity of solid 









Problem. A brass cylinder (sp. gr. 8.4) weighs 168 
air. How much will it weigh in water ? 



f. in 



SPECIFIC GRAVITY OF SOLID LIGHTER THAN WATER 21 



EXPERIMENT 11 

SPECIFIC GRAVITY OF A SOLID LIGHTER THAN WATER 

Sow many times as heavy as an equal volume of water is a 
solid which floats in water ? 



Block of wood or paraffine. 
Spring balance, or platform scales 

with weights and support. 
Jar of water. 
30 cm. rule. 



Thread. 
Lead sinker. 
Wooden cylinder. 
Support for cylinder. 



I. Sinker Method. Just as in experiment 10, it is neces- 
sary to determine the weight of the solid and the weight of 
an equal volume of water. 

Weigh the block of wood in air. 

To get the weight of an equal volume of water, since the 
object may be irregular and is lighter than water, attach a 
sinker large enough to submerge the body. The lifting 





(a) 



Fig. 12 



(b) 



22 



LABORATORY MANUAL 



effect of the water on the block is due to the weight of the 
water displaced by the block. 

To get this lifting effect of the water on the block, get the 
weight of the block in air with the sinker attached and under 
water (Fig. 12a). (It maybe more convenient to weigh 
the sinker under water and add this to the weight of the 
block in air.) Then weigh both block and sinker submerged 
(Fig. 12 5) and by subtraction get the lifting effect of the 
water on the block, i.e. weight of equal volume of water. 

Arrange the data and results as follows : 

Weight of block 

Weight of sinker in water 

Weight of block in air and sinker in water 
Weight of block and sinker both in water . . . 

Lifting effect of water on block .... 
Weight of block in air 



Specific gravity of block 



Lifting effect of water on block 



II. Flotation Method. When the object is of regular form, 
its specific gravity can often be easily determined by finding 

the fractional part of the 
whole volume which is sub- 
merged, inasmuch as the 
volume submerged repre- 
sents the weight of the 
block and the whole volume 
the weight of an equal vol- 
ume of water. 

To illustrate this method, 
use a cylinder of wood and 
float it endwise in water 
(Fig. 13). Then the specific 
gravity is equal to length 




Fig. 13 



submerged divided by the whole length. 



SPECIFIC GRAVITY OF A LIQUID 23 

Record the data and results as follows : — 

Length of stick under water cm. 

Whole length of stick cm. 

c • ., Length of stick submerged 

Specific gravity = — -£- -= — = . . . 

r 8 J Whole length of stick 

Problems. (1) A cork (sp. gr. 0.25), which weighs 
50 g. alone in air, is fastened to a sinker that weighs 200 g. 
alone in water. How much will both together weigh in 
\yater ? 

(2) A block of wood, 20 cm. x 15 cm. x 10 cm., floats in 
water. If its sp. gr. is 0.7, how many cubic centimeters are 
above water ? Which edge floats upright and how many 
centimeters of it are above the water ? 

EXPERIMENT 12 

SPECIFIC GRAVITY OF A LIQUID 

Sow many times as heavy as water is gasolene? 

Platform balance, weights and Jar of gasolene or other liquid. 

support, or spring balance. Piece of glass or porcelain. 

Glass-stoppered bottle. Thread. 

Jar of water. Cloth. 

I. Bottle Method. If we know the weight of an empty 
bottle and stopper, and then determine the weight of the 
bottle full of gasolene (or any liquid) and also the weight of 
the same bottle full of water, by subtraction we can get the 
weight of a certain volume of the liquid and also of the same 
volume of water. Then by division we get the specific 
gravity of the liquid. 

It is necessary, of course, to wipe the outside of the bottle 
dry each time and to be sure that there are no air bubbles 



24 



LABORATOBT MANUAL 



left in the bottle, i.e. that the bottle is quite full in each 
case. 

Record the weighings in tabular form : 

Weight of empty bottle with stopper . . 
Weight of bottle full of liquid (gasolene) 
Weight of bottle full of water 
Weight of liquid in bottle . . . 
Weight of water in bottle . . . 
Specific gravity of liquid . 

II. Displacement Method. If we weigh some object, like 
a glass stopper, in air and then in a liquid like gasolene, the 
loss of weight is equal, according to the Principle of Archi- 
medes, to the weight of the liquid displaced. In the same 
way, by weighing the same object in water, the loss of weight 
gives the weight of an equal volume of water. By compar- 
ing these losses in weight in the liquid and in water, we can 
determine the specific gravity of the liquid. 
Record the weighings as follows : 



Weight of glass stopper in air 
Weight of glass stopper in liquid 
Weight of glass stopper in water 
Loss of weight in liquid . . . 
Loss of weight in water .... 
Specific gravity of liquid . 



g- 
g- 
g- 
g. 

g- 



Problems. (1) A sp. gr. bottle weighs 5.25 g. empty 
and, when full, holds just 50 g. of water. How much will 
it weigh when filled with mercury (sp. gr. 13.6) ? 

(2) A glass cylinder weighs 100 g. in air and 60 g. in 
water. What will it weigh in concentrated sulphuric acid 
(sp.gr. 1.84)? 



boyle's law 



25 



EXPERIMENT 13 



BOYLE'S LAW 



How does the volume of a given quantity of gas kept at constant 
temperature vary with the pressure ? 



Boyle's Law apparatus either with 
two adjustable tubes connected by 
rubber tubing, or with a glass 
J-tube mounted on some conven- 
ient upright frame. 



Mercury. 

Millimeter cross-section 
paper. 



The closed tube (i?, Fig. 14) contains a column of air 
which is imprisoned by the mercury column. The volume 
of this air is diminished or increased by chang- 
ing the pressure upon it ; and its volume is 
determined either directly in cubic centimeters 
from the graduations on the closed tube or by 
measuring the length of the air column, assum- 
ing that the bore of the tube is uniform. 

The pressure exerted on this column of air, 
when the mercury stands at the same level in 
the two tubes, is evidently the atmospheric 
pressure. This is obtained by reading the 
barometer and is usually expressed as a certain 
number of centimeters of mercury. When, 
however, the mercury in the open tube (J.) 
stands at a lower level than that in the closed 
tube (5), then the air in the tube is under less 
than atmospheric pressure, and the pressure is 
equal to the barometer pressure (centimeters 
of mercury) minus the difference in level, also expressed as 
centimeters. But when the level of mercury in the open 




Fig. 14 



26 



LABORATORY MANUAL 



tube is higher than it is in the closed tube, then the air is 
under more than atmospheric pressure and the pressure is 
equal to the barometric pressure plus the difference in levels. 
By merely shifting the relative positions of the two tubes 
(or in the J -form of apparatus by pouring in more mercury), 
it is possible to vary the pressure on the enclosed air from 
considerably below that of one atmosphere to nearly two 
atmospheres and to observe the resulting changes in the 
volume of the air in the tube. 

Since the volume of a gas is very sensitive to changes in 
temperature, it is well not to handle the air column. In 
reading the position of the mercury on the scale, take the top 
of the mercury each time, as in reading the barometer. 
Start with the least pressure that your apparatus will give 
and gradually increase by at least six steps to the maximum. 

Record your readings and results in tabular form somewhat 
as follows, keeping only the significant figures: 



Atmospheric pressure (E 


►arometer) . 






. cm. 




V 

Volume of 
Aik 


Height of 

Mercury in 

Closed Tube (B) 


Height of 

Mercury in 

Open Tube (A) 


Difference 

in 

Levels 


P 

Pressure 


VXP 


. . . cm. 3 


. . . cm. 


. . . cm. 


. . cm. 


. . cm. 





From this experiment it will be clear that when the pres- 
sure increases, the volume decreases. Since, moreover, in 
the several trials, the product of volume times pressure is 
nearly constant, i.e. FxP=F'xP'= V n X P", it follows 
that the volume of the air in the tube varies inversely as the 
pressure. In other words when the pressure is doubled, the 
volume is halved. 



DENSITY OF AIR 27 

This relation should also be shown by plotting a curve on 
cross-section paper, using the observed pressures as vertical 
distances and the volumes as horizontal distances. 

Problem. In a certain experiment of this sort, the data 
showed that the volume of air was 25.5 cm. 3 when the pressure 
was 85.5 cm. What would have been the volume when the 
pressure was 20 lb. per sq. in.? 



EXPERIMENT 14 

DENSITY OF AIR 

What does a liter of air weigh under the conditions of tempera- 
ture and pressure of the room ? 

Two-liter round bottom flask, Screw pinchcock. 

with rubber stopper and Equal-arm balance 
connections. sensitive to 0.01 g. 

Air pump. Set of weights. 

Mercury gauge. Barometer. 

First of all, it is assumed that the volume of the flask 
has been determined by filling it with water and then meas- 
uring the volume of water with a graduate. When this 
volume has once been determined, it is marked on the flask 
and this part of the experiment need not be repeated ; but 
great care should be taken to have the flask dry and clean 
inside and out before attempting to weigh its content 
of air. 

Connect the flask, mercury gauge, and air pump as in- 
dicated in the diagram (Fig. 15). After pumping out some 
of the air, pinch the rubber tube connected with the pump 
and watch the mercury gauge to see whether there is a leak 
in the connections. A gradual drop of the mercury would 



28 



LABORATORY MANUAL 



Air Pump 



indicate such a leak, which must be stopped before proceed- 
ing. When all the connections are tight, continue pump- 
ing for at least five minutes and then read the mercury gauge 

{i.e. height of mercury in 
tube above that in glass). 
Close the pinchcock (jP) 
near the bottle tight. 

Disconnect the flask 
with its tube and pinch- 
cock, suspend it from one 
arm of the balance, and 
counterpoise its weight 
with great care. Without 
disturbing the flask or 
balance, open the pinch- 
cock and let the air in. 
Add the necessary weights 
to make up for the air 
admitted. This added 
weight represents the 
weight of air admitted to the flask. But not quite all the air 
was removed from the flask by the pump. In fact, only that 
fraction of total volume of the flask indicated by the height 
of mercury in the pressure gauge divided by the height of 
mercury in the barometer, was removed. 

Having calculated, then, the number of cubic centimeters 
of air admitted and its weight, we may readily compute the 
weight of 1000 cm. 3 . 

Since the weight of air varies greatly with the temperature 
and pressure, it is well to record the room temperature and 
barometric pressure and then check the experimental result 
of this rather crude method with the results given in the 
tables in the Appendix. 




Fig. 15 



SPECIFIC GRAVITY OF A LIQUID 



29 



Arrange the data and calculated results in an orderly 
fashion and draw a diagram of the apparatus. 

Problem. If one cubic foot of air weighs about 1.3 ounces, 
how many pounds of air are contained in a schoolroom which 
is 40 feet x 30 feet x 12 feet? 



EXPERIMENT 15 



SPECIFIC GRAVITY OF A LIQUID BY BALANCING 

COLUMNS 

« 

How many times as heavy as water is a saturated solution of 

blue vitriol as indicated by the heights to ^ >. 

which the atmospheric pressure will raise || || 

columns of these liquids ? 



Two glass tubes about 
80 cm. long. 

Glass T-tube with rub- 
ber connections. 

Screw pinchcock. 



Tumbler of water. 
Tumbler of solution of 
blue vitriol (CuS0 4 ). 
Meter stick. 



Support the T-tube (Fig. 16) at such a 
height that the ends of the glass tubes will 
nearly reach the bottoms of the tumblers. 
Suck out some of the air from the tubes 
until the water rises about 60 cm. and then 
close the screw pinchcock (P). Observe 
carefully the levels of the liquids to see if 
the apparatus is leaking, as will be shown 
by a gradual drop of the liquids in the 
tubes. 

It is evident that the pressure of the air 
on the liquids in the tumblers is holding 




30 



LABORATORY MANUAL 



up the two columns, and the pressure is just balanced by- 
pressure of the liquid in the tubes plus the air above. That 
is, each liquid column exerts the same pressure at its base. 
It is also evident that this pressure depends on the height 
and density of the liquid, so the liquid of less density will 
have the greater height ; in other words, the densities of the 
two liquids (A and i?) vary inversely as the heights of the 
columns (x and y). So that 

Specific gravity of blue vitriol solution = Density of blue vitriol 

Density of water 

_ Height of water column 
Height of blue vitriol column 

To obtain these heights we shall need to make the follow- 
ing measurements and computations : 





Trials 




#1 


#2 


#3 


Height of water column above the table .... 
Height of water in tumbler above the table . . . 

Net height of water column raised * 

Height of blue vitriol column above the table . . 
Height of blue vitriol in tumbler above the table . 

Net height of blue vitriol raised * 

Specific gravity of blue vitriol 

















* Note. Subtract from the height of each column, as measured, the height 
to which it was raised by capillary action at the beginning. 

Problem. How high would a glycerine barometer (such 
as is in the South Kensington Museum, London) stand, 
when the mercury barometer reads 30 inches ? Sp. gr. of 
glycerine = 1.26. Sp. gr. of mercury = 13.6. 



PABALLELOGBAM OF FOBCES 



31 



EXPERIMENT 16 

PARALLELOGRAM OF FORCES 

When three non-parallel forces are acting on a body, what must 
be their relative directions and magnitudes in order to pro- 
duce equilibrium ? 



Three spring balances. 
Three clamps. 
30 cm. ruler. 



Fishline. 
Block of wood. 



To the middle of a piece of fishline about 40 cm. long tie 
a second piece about half as long. At each of the free ends 
make a loop and attach the hook of a spring balance. To 
the ring of each balance attach a strong string, and then 
arrange the clamps, balances, and strings as shown in Fig. 17. 

Pull each balance until its index is about in the middle of 




Fig. 17 



32 LABORATORY MANUAL 

the scale where it is most reliable, and then slip a page of the 
notebook under the cord connecting the balances, so that 
the knot conies about in the middle of the page. 

In order to show the direction of each cord on the paper, 
place a rectangular block alongside and draw a line directly 
under each cord. Record on each line the pull indicated by 
the balance, and then relieve the tension on the spring bal- 
ances. Observe the zero reading of each balance and apply 
the proper correction to the reading just recorded. If the 
zero reading is less than zero, add the correction to the bal- 
ance reading recorded on the paper ; if it is more than zero, 
subtract the proper amount. 

If the experiment has been carefully done, the three lines 
representing the three forces will, when prolonged, intersect 
at a common point. Measure off on each line a distance 
corresponding to the force, according to any convenient scale, 
such as 200 g. to 1 cm. Make an arrowhead at the end 
of each measured line and erase that part of each line which 
lies beyond the arrowhead. 

On any two of these lines construct a parallelogram, 
using a ruler and compass to get the lines exactly parallel. 
Draw the three original force lines as solid lines ( OA, OB, 
and 00) and the lines needed to complete the parallelo- 
gram (BR and OR) and the diagonal ( OR) as broken or 
dotted lines. Draw the diagonal of this parallelogram 
from the central point, measure its length, and compute the 
magnitude of the force which it represents. For example, 
a line 15.6 cm. long represents a force of 3120 g. when the 
scale is 200 g. to 1 cm. This diagonal line represents the 
resultant of the two forces which form the sides of the par- 
allelogram. 

How does the resultant of two forces compare with the third 
force (a) in magnitude and (b) in direction? 



FORCES ACTING ON A SIMPLE TRUSS 



33 



Problem. Find the direction and magnitude of a force 
needed to balance the effect of 12 lb. acting north and 16 lb., 
east. 

EXPERIMENT 17 

FORCES ACTING ON A SIMPLE TRUSS 



How much is the thrust 
exerted by a simple stick 
when used with a " tie " 
to support a weight? 

Stick with foot support 
(Pratt Inst, model). 
Two spring balances. 
Scale pan and weights. 
Large protractor. 

Set up the apparatus 
as shown in Fig. 18, so 
that the stick BO is not 
horizontal. Add enough 
weights at L to stretch the 
balance F nearly to its full 
scale reading. The weight 
of the stick itself may be 
neglected because it is so 
small in comparison with 
the other forces. 

Measure w r ith a large 
protractor the angles BCL 
and ACL and record the 
weight at L. 

To find the tension in 




Fig. 18 



34 



LABORATORY MANUAL 



AC, draw a careful diagram of the three forces with the 
force OL to some convenient scale. Compare the result of 
this computation with the reading of the balance F. 

Also by the same diagram, compute the compression on 
the stick BO. To test this, attach a second balance at 
and pull out in the line of the stick B O until the end of the 
stick at B just leaves the wall. Compare this pull (#) with 
the computed compression in the stick BO. 

Change the angle of the stick to the wall and repeat the 
experiment, making the necessary diagrams and taking check 
readings as before. 

Record the readings also in tabular form as follows : 





Case 


L 


ABCL 


/.ACL 


F 


S 


Computed 


Measured 


Computed 


Measured 


I 
















II 



































Problem. If the stick BO is 10 ft. long and is placed at 
an angle of 45° to the wall, what is the tension in the tie 
OA which is horizontal when the load is 2 tons ? What is 
the compression in the stick BO? 



BREAKING STRENGTH OF WIRE 35 

EXPERIMENT 18 

BREAKING STRENGTH OF WIRE 

Sow many kilograms of force are required to break No. 27 
spring brass wire, steel wire, and copper wire ? 

Wire-breaking apparatus (Fig. 19). Spools of steel, 

10 kg. spring balance. brass, and copper wire, # 27. 

Micrometer. 

The apparatus (Fig. 19) is so designed that the tension 
on the wire at the instant it breaks, is recorded on a spring 
balance (i?). The tension is applied by means of a crank 




(<7) which turns an axle on which the wire is wound. The 
other end of the wire is attached to the spring balance by 
means of a frame. As this frame is pulled, a wedge (IF) 
drops down which holds the index of the balance just where 
it was at the instant of breaking. 

First slip one end of the wire through the hole in the 
crank shaft and bend the end over sharply so as to extend 
along the shaft. In this way one or two turns of the handle 
will cause the wire to wind over the end and so fasten it 



36 LABORATORY MANUAL 

securely. Pass the other end of the wire a couple of times 
around the wooden post on the sliding frame and clamp the 
end under the binding post. Let the w r edge rest lightly in 
the slot of the sliding frame. Set the pawl (P) so that it 
will rest on the toothed wheel attached to the shaft and so 
prevent the shaft from turning backward. 

Now turn the crank slowly and cause a slight tension in 
the wire. Measure with a micrometer the diameter of the 
wire in at least two places, and increase the tension on the 
wire by turning the crank and keeping the wedge down in 
the slot until the wire breaks. As the wedge fills the slot, 
it holds the spring balance at just the position it was in 
when the wire broke. Record this force in kilograms. 

Repeat the experiment twice and find the average of the 
three readings for the breaking strength of ^ 27 brass wire. 
If time permits, try also steel wire and copper wire. 

Problem. From the result of your experiment calculate 
the force in kilograms needed to break a wire of the same 
material 1 mm. 2 in cross section. 



BENDING OF BODS 



37 



EXPERIMENT 19 



BENDING OF RODS 

How does the bending of a rod vary under different loads? 
How is the bending affected, (a) if the rod is shortened to 

one half its original length, (b) if the rod is doubled in width, 

(c) if it is doubled in thickness ? 



Rods of wood, steel, or brass 
110 cm. x 1 cm. x 1 cm. 

Rods of same material but 
110 cm. x 2 cm. x 1 cm. 

A Supports. 



Indicator lever, or micrometer screw 

with cell and telephone receiver. 
Vertical scale. 
Set of weights. 
Pan for weights. 



Board to support apparatus. Meter stick. 

Place the board across the gap between two laboratory 
tables and set up the apparatus as shown in Fig. 20. Of 
course we should expect a rod to bend more with a heavy 




\U 





Fig. 20 

load than under a light one, and so in this experiment we 
will try to show just how this bending varies with various 
loads (Z). Since the rod gets a permanent "set" or bend, 
when loaded beyond a certain point, called the " elastic 
limit," we must each time remove the load and read the zero 
point. The amount of the deflection or bending which a rod 
will stand and still recover is very small, and so some special 



38 



LABORATORY MANUAL 



method has to be adopted to measure this deflection, such as 
a magnifying lever (Fig. 20) or a micrometer screw (Fig. 21). 




Fig. 21 

Record the loads and deflections of the rod in tabular 
form somewhat as follows : 



I. Length eetween Supports 100 cm. Width 1.0 cm. 
Thickness 1.0 cm. 





Load 


Indicator Readings 


Actual 
Deflection 


Deflection per 


Before loading 


After loading 


100 G. 


100 g. 
200 g. 
300 g. 
400 g. 
500 g. 











BENDING OF RODS 



39 



II a. Length between Supports 50 cm. Width 1.0 cm. 
Thickness 1.0 cm. 



500 g. 
1000 g. 










II b. Length between Supports 100 cm. Width 2.0 cm. 
Thickness 1.0 cm. 


200 g. 

400 g. 


! 




II c. Length between Supports 100 cm. Width 1.00 cm. 
Thickness 2.0 cm. 


500 g. ! 
1000 g. 











From a comparison of the results shown in the last column 
under "Deflection per 100 g.," in case I, state how the deflection 
varies with the load. 

By comparing the average deflection per 100 g. in cases I 
and II a, state how the hending decreases when the length is 
halved. 

By comparing the average deflection per 100 g. in cases I and 
115, state how the bending decreases when the width is doubled. 

Finally by comparing the average deflection per 100 g. in 
cases I and II <?, state how the bending decreases when the depth 
is doubled. 

Note . If metal rods are used with a micrometer screw and heavier loads, 
which are needed, the results will be more consistent. 

Problem. If a beam 10 ft. long, 4 in. wide, and 6 in. 
thick, is bent 0.5 in. under a load of 300 lb., how much load 
would it take to bend a beam 5 ft. long, 2 in. wide, and 3 in. 
thick, the same amount ? 



40 



LABORATORY MANUAL 



EXPERIMENT 20 



ACCELERATED MOTION 



How does the distance traversed by a moving body under con- 
stant acceleration vary with the time? 



Grooved plank according to 

Duff. 
Steel ball, 1.5" diam. 
Blocks to support one end of 

incline. 



Meter stick. 

Pepper box with lycopodium 

powder. 
Cloth. 



When the grooved plank (Fig. 22) is placed horizontally 
on the table, a steel ball placed on one edge will, when re- 
leased, oscillate back and forth like a pendulum. Although 




Fig. 22 

the swings decrease in amplitude, yet the time of each swing 
remains constant. When the plank is tilted so that one end 
is higher than the other, a ball placed at the top in the 
middle of the groove will roll down, going faster and faster 
until it reaches the bottom. 

In this experiment we shall combine this oscillatory motion 
back and forth across the groove with the accelerated motion 
down the incline in such a way as to make the oscillatory 
motion mark off equal intervals of time for the study of the 
accelerated motion. 

First wipe off the trough with a damp cloth and rub it 
thoroughly dry, then sprinkle it with lycopodium powder. 



ACCELEBATEB MOTION 



41 



Tilt the plank with blocks, taking care to keep the under 
edges at the upper and lower ends exactly horizontal. Place 
the ball at the top of the groove against the metal 
strip ($) which serves as a guide until it reaches the 
middle line. When the ball is released, it goes zig- 
zagging down the groove. If the powder is blown 
off, we see distinctly the path traced on the black- 
board, somewhat as shown in Fig. 23. We have now 
simply to measure certain distances along the mid- 
line to understand the relation of distance to time in 
a case of accelerated motion. 

In the second column we record the distances trav- 
ersed in 1 interval of time, 2 intervals, 3, and so on, 
that is, AB, AC, AD, AE, etc. 

In the third column we record the separate dis- 
tances covered in the 1st interval of time, in the 2d 
interval, and so on, that is, AB, BO, (7D, etc. 

From a study of the result given in the fourth col- 



umn [—J, what relation seems to exist between the space, 
s, and the time, t? From a study of the results in the 

last column ( ], what relation seems to exist be- fig. 23 

\2t-lJ 

tween the separate distances (c?) and the odd numbers given by 
the expression (2 t — 1)? 



Time 


Space 
Traversed (s) 


Distance covered 

in Each Time 
Interval (d) 


s 
P 


d 


Intervals (t) 


02* -1) 


1 










2 










3 










4 










5 











42 LABORATORY MANUAL 

Problem. As the board is tilted more and more, the value 

— increases, until when the board is vertical and the ball falls 
t 2 

freely, — = 16.1, where' t is expressed in seconds and s in feet. 
How far would a body fall freely in 3 seconds? 



EXPERIMENT 21 

THE FIXED POINTS OF A THERMOMETER 
How to test the fixed points of a thermometer, i.e. 0° and 

ioo° a 

How much is the boiling point of water affected by a change of 
1 centimeter in the barometric pressure ? 

Steam boiler and Bunsen burner. Small glass tumbler. 

Mercury U-tube gauge. Cracked ice (clean). 

Thermometer (— 10° to 110° C). Screw pinchcock. 

Fill the boiler about half full of water, screw the chimney 
or top down firmly, and attach the necessary gauge (Fig. 24). 
Open up the pinchcock (A) near the top of the chimney 
and start heating the water. 

I. Freezing Point. Fill a glass tumbler with clean cracked 
ice and pour over it enough water to fill the spaces around 
the pieces of ice. Put the thermometer bulb down into the 
melting ice, so that you can just see the mercury. After a few 
minutes, when the mercury has ceased to fall and has come 
to a definite position, read the thermometer to one tenth of 
a degree, and record this as the freezing point of your ther- 
mometer. The error is the difference between this reading 
and zero. 

II. Boiling Point. Carefully insert the thermometer in 
the stopper of the steam boiler, so that the 100° mark on 



THE FIXED POINTS OF A THERMOMETER 



43 



the scale projects just a little above the stopper. Let the 
steam flow around the bulb and stem for several minutes 
until the thermometer has come to a fixed reading, then, 
read and record its position and also the barometer height. 




Fig. 24 



III. Pressure of Steam and its Temperature. Since the 
boiling point of water is much affected by changes in pres- 
sure, it has been necessary to fix on some standard barometric 
pressure, and this is 760 mm. As the barometer is very sel- 
dom just at this point, it is necessary to know how to com- 
pute the true boiling point of water at any pressure. To 
do this we need to know the effect on the temperature of 
steam of a change in pressure of 1 cm. 

When the steam is escaping freely into the air, the mer- 
cury in the gauge ((r) reads the same in each arm. Now 



44 LABORATORY MANUAL 

gradually close the steam exit (A) by screwing up the 
pinchcock until the pressure gauge shows a difference in 
levels of about 6 or 8 cm. and has become fairly steady, then 
read the thermometer, and remove the burner. 

How much has the temperature of the steam been raised by 
increasing the pressure ? 

Hoiv much is the temperature of steam raised per centimeter 
increase of pressure? 

Very careful and repeated experiments of this sort have 
shown that the temperature of steam is changed about 0.37° 
for each centimeter of change of pressure. Compute, then, 
the true temperature of steam to-day and then the error in 
your thermometer. 

Problem. A standard thermometer was found on a certain 
day to read in steam 98.5° C. ; what was the pressure ? 

EXPERIMENT 22 

LINEAR EXPANSION OF A SOLID 

How much does one centimeter of aluminum expand when 
heated one degree Centigrade ? 

Linear expansion apparatus according Thermometer. 

to Hall or Co wen. Barometer. 

Boiler and burner. Meter stick. 

Since the amount which a solid expands is exceedingly 
small, it is difficult to measure it with great precision. One 
of the many methods of measurement of this slight expan- 
sion makes use of a lever to magnify the actual expansion as 
shown in Fig. 25.* The metal tube is heated by passing 

* This form of apparatus was designed by Mr. C. M. Hall of Springfield, 
Mass. 



LINEAR EXPANSION OF A SOLID 



45 



steam through it. One end of the tube is made fast with a 
pin (P), and the other end, as the rod expands, turns a bent 
lever (£) about a point (A). The expansion of the tube 



Steam 



'^^ 



r 



A Fig. 25 

is magnified as many times as the short arm (AB) of the 
lever is contained in the long arm (CD). Therefore to get 
the actual expansion we have only to divide the movement 
of the pointer by the magnifying power of the lever. 

In another form of apparatus the expansion is measured 
by allowing the tube (T) to rest on a needle (iV), which in 
turn rests on roller bearings (BB) as shown in Fig. 26.* 




Fig. 26 

The rotation of the needle is measured on a circular scale by 
a pointer. Evidently if the needle turns around once, the 
tube has expanded a distance equal to the circumference of 
the needle ; and if it turns less than a complete revolution, 
the tube has expanded the corresponding fraction of the 
circumference of the needle. 



* This form of apparatus was designed by Mr. G. A. Co wen of Jamaica 
Plain, Boston. 



46 LABORATORY MANUAL 

In the first method the short arm of the bent lever, and 
in the second method the diameter of the needle, can be meas- 
ured with great precision by means of a micrometer. 

The length of the tube between the fixed point (P) and 
the indicating device can be easily measured to three signifi- 
cant figures with an ordinary meter stick. 

The temperature of the tube at first may be assumed to be 
that of the room, and the temperature of the tube when hot 
will be the temperature of steam, which can be computed 
from the barometric reading. 

Record the measurements and computations somewhat as 
follows : 

Length of metal tube cm. 

Temperature of room °C. 

Height of the barometer mm. 

Temperature of steam °C. 

Length of short arm of pointer . . . , cm. 

Length of long arm of pointer cm. 

Magnifying power of pointer 

Reading of pointer before cm. 

Reading of pointer after cm. 

Rise of the pointer cm. 

Actual expansion of the metal tube cm. 

Expansion of tube per degree rise in temperature . . cm. 
Expansion of one centimeter of tube per degree 

(coefficient of linear expansion) 



o 



Problem. If the melting temperature of aluminum is 1157 
F., how much must be allowed for shrinkage in making 
patterns for aluminum castings? (For coefficient of ex- 
pansion of aluminum, see tables in Appendix.) 



CUBICAL EXPANSION OF AIR 47 

EXPERIMENT 23 

CUBICAL EXPANSION OF AIR 

What fraction of its volume at 0°(7. does a certain quantity of 
air expand when heated 1° (?. under constant pressure ? 

Glass tube of dry air according Boiler with top. 

to Waterman. Bunsen burner. 

Thermometer. Pail or battery jar of cracked ice 

Meter stick. or snow. 

A thick-walled glass capillary tube with a uniform bore 
of about 1 mm. is closed at one end (Fig. 27). Near the 
middle of the tube is a thread of mercury (M) about 
2 cm. long. The distance QA3T) from the closed end 
of the bore up to the mercury represents the volume 
of air. (The volume of the air is measured in terms 
of the volume of a unit length of the tube.) 

Stand the air tube in the battery jar so that the air 
column is surrounded by cracked ice and allow it to 
stand until the mercury index ceases to go down fur- ||L f 
ther. Then mark the position of the lower end of the 
thread of mercury with a rubber band. Remove the 
tube from ice, lay it alongside the meter stick, and 
measure the distance from the closed end of the bore 
to the rubber band. This represents the volume of 
the air at 0° C. 

Now put the air tube into the top of the steam 
boiler, in such a way as to surround the air column 
with steam. When the mercury ceases to rise in the tube, 
again mark the position of the lower end of the mercury 
with a rubber band. Remove the tube from the boiler and 
measure the distance, which is the length of the air column 



'A 
Fig. 27 



48 LABORATORY MANUAL 

when hot. Read the barometer and compute from this the 
temperature of the steam. 

Compute the expansion of the air, the rise in temperature, the 
expansion per degree rise in temperature, and finally the ex- 
pansion of 1 cm. per degree. This last result represents the 
coefficient of cubical expansion of air. 

Problem. A room 20 m. x 10 m. x 5 m. would contain 
1290 kg. of air at 0° C. ; how much air will it contain at 30° C? 



EXPERIMENT 24 

SPECIFIC HEAT OF A METAL 

How many calories does one gram of a metal give out 
in cooling l°C.f 

Blocks of metal, such as aluminum, Thermometer. 

brass, or copper. Platform balances and 

Boiler and burner. sets of weights. 
Calorimeter. 

The thermal unit commonly employed in heat measure- 
ments in the laboratory is the calorie. This is the amount of 
heat needed to raise the temperature of one gram of water 
one degree Centigrade. Experience shows that more heat 
is required to heat one gram of water one degree than is re- 
quired to heat one gram of almost any substance one degree. 
To find out just what fraction of a calorie is absorbed or 
given out when one gram of a metal changes its temperature 
one degree is the purpose of this experiment. 

If hot metal is plunged into cold water, the metal gives 
out heat and the water absorbs heat ; and if no heat is 
lost during the process, the number of calories given out 



SPECIFIC HEAT OF A METAL 49 

by the metal is equal to the number of calories absorbed 
by the water. But it must also be remembered that the 
vessel which holds the water, the calorimeter, absorbs heat. 
Experiments show that brass (the metal commonly used for 
the calorimeter) absorbs about one tenth as much heat as the 
same weight of water. Therefore one tenth the weight of 
the calorimeter, called the water equivalent of the calorimeter, 
is to be added to the weight of water used. 

To compute the number of calories absorbed by the water 
and calorimeter, multiply the number of grams of water plus 
the water equivalent of the calorimeter by the number of 
degrees which it is raised in temperature. This quantity of 
heat was furnished by a certain number of grams of metal 
in cooling a certain number of degrees. From this we can 
compute how much heat was furnished by one gram of metal 
in cooling one degree. This is called the specific heat of the 
metal. 

The metal for this experiment may be finely divided like 
shot, which may be heated in a dipper set in a boiler, or per- 
haps more conveniently may be in the form of a cylinder or 
ball which is heated directly in the water of the boiler. 
Weigh the metal and then put it into the boiler to heat. In 
the meantime measure out a certain quantity of cold water, 
about 300 cm. 3 at from 5° to 10° C. Record the weight of 
water used, considering 1 cm. 3 as equal to 1 g. 

When the metal has reached the temperature of the boil- 
ing water, which is to be computed from the barometric 
reading, first read and record the temperature of the cold 
water and then quickly lift the metal by means of a thread 
out of the boiler and put it in the cold water. Stir the 
water and take its final temperature as soon as it becomes 
constant. 

These data should be recorded in tabular form. 



50 



LABORATORY MANUAL 



Weight of metal g. 

Weight of cold water . . . . g. 

Weight of calorimeter g. 

Temperature of metal °C. 

Temperature of cold water ° C. 

Temperature of water and metal °C. 



From these facts calculate the following results : 

Water equivalent of calorimeter 

Weight of water and water equivalent of cal. 
Rise of temperature of water and calorimeter 
Calories absorbed by water and calorimeter 

Drop in temperature of metal 

Calories given out by metal in cooling 1° C. 
Calories given out by 1 g. of metal in cooling 1° C 



g- 
g- 

°C. 
cal. 
°C. 
cal. 
cal. 



What do you find the specific heat of the metal used to be? 
Compare this with the result given in the tables in the Ap- 
pendix and try to explain the difference. 

Note. Experiments in heat measurements are especially difficult and 
great precautions must be taken. Each time read the thermometer correctly 
not only to whole degrees, but also to tenths of a degree. Avoid han- 
dling the calorimeter during the experiment or in any way transferring heat 
to or from it. Check up each step in the arithmetical computation. 



Problem. A 10-gram ball of platinum (sp. ht. 0.04) is 
taken from a furnace and dropped into 40 g. of water at 
10° C. The temperature is raised to 25° C. How hot was 
the furnace ? 



COOLING CURVE THROUGH THE MELTING POINT 51 

EXPERIMENT 25 

COOLING CURVE THROUGH THE MELTING POINT 

Sow does a change of state, such as from a liquid to a solid, 
affect a cooling curve ? 

Test tube and clamp. Acetamide or naphthaline. 

Bunsen burner. Millimeter cross-section paper. 

Thermometer. Boiler. 

Fill a test tube about three quarters full of acetamide and 
place the tube down in the boiling water of the boiler. In- 
sert the thermometer in the test tube and heat until all the 
crystals are melted and the liquid has reached a temperature 
of about 100° C. Then lift the test tube out of the boiler 
and clamp it in a convenient position to observe the tempera- 
ture as the liquid cools. Do not disturb the liquid or ther- 
mometer in any way. 

As the substance cools from 100° C. to 50° C, record every 
half minute the temperature and the time. Then plot these 
results on cross-section paper, representing temperatures by 
vertical distances (1 mm. for 1°) and times by horizontal dis- 
tances (4 mm. for 1 min.). Study the curve carefully so as 
to answer such questions as the following : 

(a) What portion of the curve represents the cooling of the 

substance in the liquid state ? 

(b) What portion of the curve represents the condition dur- 

ing the process of crystallization ? 

(c) What portion of the curve represents the cooling of the 

substance in the solid state ? 

(d) Is there any part of the curve which indicates " subcool- 

ing " t 

(e) What would you consider the freezing point of the sub- 

stance used? 



52 



LABORATORY MANUAL 



Question. Does the process of freezing water evolve or 
absorb heat from the surroundings ? 

EXPERIMENT 26 



LATENT HEAT OF MELTING ICE 

How many calories are required to change one gram of ice at 
0° 0. into water at 0° 0. ? 



Calorimeter. 

Thermometer. 

Platform scales and set of weights. 



Supply of hot water (teakettle). 
Cracked ice. 
Cloth or towel. 



First weigh the calorimeter empty and then with about 
300 g. of warm water, the temperature of which is about 
25° C. above that of the room. Break or grind up enough 
clean ice to fill a 150-cm. 3 beaker with pieces less than 2 cm. 
in diameter. Stir the water in the calorimeter thoroughly 
and determine its temperature as precisely as possible. At 
once add the ice, taking care to wipe each piece on the cloth 
and not to spatter the water. Stir the water continually, 
and when the temperature of the water has fallen 10° or 
more below that of the room, stop adding ice and just as soon 
as the last piece melts, read the temperature again with great 
precision. To find out how much ice has been used, weigh 
the calorimeter with its water and melted ice. 

Record the following data : 

Weight of calorimeter (c) . . 
Weight of calorimeter + water 

Weight of water (w) 
Initial temperature of water (/) 
Final temperature of water (?) 
Weight of calorimeter + water + ice 

Weight of ice (i) .... 



C C. 
°C. 



LATENT HEAT OF STEAM 53 

The water and calorimeter in cooling give out heat which 
is used, first, to melt the ice, and, second, to raise the water 
which is formed, from zero to the final temperature. If each 
gram of ice in changing from ice at 0° C. to water at 0° C. 
requir.es x calories, then i grams of ice would require ix 
calories. But after the ice is melted, it becomes i grams of 
water at 0°C, and this water is raised to the final tempera- 
ture t' which requires it 1 calories in addition. This heat is 
supplied by W grams of water and by c grams of calorimeter 
(whose specific heat is about 0.1) in cooling from the initial 
temperature t to the final temperature th This heat is equal 
to (w + 0.1 c.) (t — £') calories. If we make an equation 
between the heat absorbed by the ice and the heat given out by 
the water and calorimeter, we can easily solve for x, the latent 
heat of melting ice. 

Problem. If the latent heat of melting ice is 80 calories, 
how many B. t. u. are needed to melt 1 lb. of ice ? 



EXPERIMENT 27 

LATENT HEAT OF STEAM 

How many calories of heat are liberated when one gram of 
steam at 100° O. condenses into water at 100° C? 

Boiler and burner. Calorimeter. 

Water trap. Thermometer. 

Balance and weights. 

Fill the boiler half full of water and start heating. Then 
fill the calorimeter, whose weight has already been deter- 
mined, two thirds full of cold water (about 5° C), and 
determine the weight of the water with great precision. 



54 



LABORATORY MANUAL 




Fig. 28 



Set up a book or wooden screen between the boiler and 
calorimeter and place a thermometer in the water. 

As soon as the steam is ready, attach the water trap (T, 
Fig. 28) to the delivery tube to catch any condensed steam. 

Stir the water in the calorimeter 
with the thermometer and read 
its temperature to one tenth of a 
degree. Then quickly put the de- 
livery tube of the water trap (T 7 ) 
into the water so that its end pro- 
jects under water about 2 cm. 
Continue to stir the water slowly 
until the water gets to a tempera- 
ture about as much above that 
of the room as the initial temperature was below it. Re- 
move the delivery tube from the calorimeter and after 
stirring read the highest temperature which the water 
reaches. 

Finally, as soon as convenient, weigh with great care the 
calorimeter, water, and condensed steam and compute the 
weight of the steam used. 
Record the following data : 

Weight of calorimeter (c) . . 
Weight of calorimeter + water 
Weight of water (w) . . . 
Initial temperature of water (t) 
Final temperature of water (t') 
Weight of cal. + water + condensed stea 
Weight of condensed steam (s) . . . 
Water equivalent of calorimeter (0.1 c.) 



°C. 

°c. 
g- 



g- 



Computation : 

(a) How many degrees was the water raised in tempera- 



ture? 



LINES OF MAGNETIC FORCE 55 

(6) How many calories have the calorimeter and water 
received ? 

(<?) How many grams of steam were condensed ? 

(d) How many calories did s grams of condensed steam 
give out in cooling from 100° C. to t'° C. ? 

(e) How many calories did the s grams of steam give out 
in condensing ? 

(/) How many calories did one gram of steam give out 
in condensing to water at 100° C. ? 

Problem. How many B. t. u. are required to change 100 
pounds of water at 45° F. into steam at 212° F. ? (Assume 
the latent heat of steam to be 540 cal. for 1 g. of water at 
100° C). 



EXPERIMENT 28 

LINES OF MAGNETIC FORCE 

What is the direction of the lines of magnetic force which are 
produced by the earth and a bar magnet? 

Bar magnet (15 cm. x 1 cm. x 1 cm.). Thumb tacks. 

Tracing compass (Hahn form). Hard, sharp lead pencil. 

White paper. 

Fasten a sheet of white paper to the table with thumb tacks 
and lay the magnet on the paper near the middle so that its 
axis lies nearly north and south and its north-seeking pole is 
turned toward the south. Trace around the bar magnet 
with a pencil and mark the position of its poles with the 
letters N and S. Indicate with dots the starting points of 
about a dozen lines of magnetic force, grouping them mostly 
around the N-pole. 



56 



LABORATORY MANUAL 




Fig. 29 



Place the tracing compass on the paper near the magnet in 
such a way that the S-pole notch in its rim (see Fig. 29) 
lies as nearly as possible right over a starting point, and then 
turn the compass around this point until 
the needle stands exactly over the line on 
the compass base. Then mark with a lead 
pencil the position of the N-pole notch in 
the rim. Move the compass in the direc- 
tion in which the N-pole points until the 
S-pole notch lies exactly over the mark 
that has just been made. Then turn as 
before the compass about this point until 
the needle lies exactly over the north- 
south line made on the bottom of compass, and again mark 
the position of N-pole notch. Continue this until the edge 
of the paper is reached. Connect all these points with a 
line of dashes and arrows to show the path and direction of 
the compass. Such a line is called a magnetic line of force. 

Draw other lines of force, beginning each time with a 
point near the N-pole of the magnet. 

Draw lines of force which start on the south edge of the 
paper but do not hit the magnet at all. 

On another sheet of paper, repeat this experiment with the 
S-pole pointing south. 

Fold up the sheets of paper and glue them into the regular 
notebook. 

Questions. Are there any points in the magnetic field 
about the bar magnet where the force of the earth and mag- 
net are exactly equal but opposite in direction ? How did 
you detect them ? 



THE VOLTAIC CELL 



57 



EXPERIMENT 29 



THE VOLTAIC CELL 



How can chemical energy he converted into electrical energy ? 



Glass tumbler. 

Zinc strip, unainalgamated. 

Zinc strip, amalgamated. 

Copper strip. 

Board top for tumbler. 

2 binding posts. 

Sulphuric acid (1 : 20). 

Commercial sal-ammoniac cell. 



Connecting copper wire. 

Simple galvanoscope. 

Large copper plate. 

Zinc wire. 

Porous cup. 

Copper sulphate solution. 

Zinc sulphate solution. 



I. Action of Dilute Sulphuric Acid on Copper and Zinc. 

(1) Open circuit. Fill a tumbler about three fourths full of 
dilute sulphuric acid (1 to 20) and put a strip of copper 
and a strip of zinc into the acid in such a way as to avoid 
all metallic connections between the strips. Observe for a 
few minutes the action of the acid on each strip and then 
record just what is seen on the 
surface of each metal. (The bub- 
bles are hydrogen.) 

(2) Closed circuit. Connect the 
tops of the strips (Fig. 30) and 
notice what change, if any, takes 
place on the surface of each metal. 
Record the results. FlG - 3° 

II. Effect of using Amalgamated Zinc. Replace the or- 
dinary zinc which has just been used by an amalgamated 
zinc plate or rod (i.e. zinc which has been dipped in mer- 
cury and rubbed until it is covered with a smooth coating 
of mercury). Repeat the experiment with the circuit open 




58 



LABORATORY MANUAL 




Fig. 31 




and closed, and record any differences which are observed in 
the action. 

III. Magnetic Effects observable about the Wire connect- 
ing the Strips. Place a very simple form of galvanoscope 
(coil of wire with compass in the center, Fig. 31, a or J) so 

that the plane of the coil is north 
and south. Connect the binding 
posts of the metal strips by means 
of copper wire to 
the binding posts of 
the 15- or 25-turn 
coil of the galvan- 
oscope. Assuming 
that the current 
comes from the cell 
by way of the copper strip, note the direction of the current 
as it goes over the top of the galvanoscope coils and the posi- 
tion of the needle. Reverse the currents in the coils by 
interchanging the wire connections of the galvanoscope. 
Observe the new position of the needle due to the change 
in direction of the current. 

IV. Polarization of a Simple Cell. Set up the cell as used 
in III, but use a copper plate of large surface (rolled into 
cylindrical form) and a very narrow strip or wire of zinc. 
Arrange the coils of the galvanoscope so that the coils are 
north and south, and turn the compass so that its zero is 
directly under the north end of the needle. When all the 
connections are made, immerse the plates in the acid and 
read the deflection of the needle as soon as it stops swinging 
violently. (If this deflection is more than about 45° insert 
into the circuit enough No. 36 German silver wire to reduce 
the deflection to about 40°.) Tap the galvanoscope lightly 



THE VOLTAIC CELL 



59 






E3 


Nut 


_=^ 


=£~HI 


s 






~fz 


3= 


^^ 


-:^ 


d^fl 


fe 





Fig. 32 



This is known as 



to allow the needle to take its proper position. Watch the 
needle carefully for two minutes and record what you ob- 
serve. Short-circuit the cell for half a 
minute by holding a stout, short copper 
wire in contact with both the copper and 
zinc plates (Fig. 32). Of course the de- 
flection is reduced nearly to zero because 
most of the current now goes through the 
stout copper wire. Remove this wire and 
see if the needle returns quite to its old 
value. By short-circuiting the cell, the 
hydrogen was generated in greater abun- 
dance. Judging from this experiment, 
what effect does an accumulation of hy- 
drogen upon the copper plate seem to 
have upon the strength of the current ? 
the polarization of the cell. 

V. Daniell Cell. Replace the simple cell with a Daniell 
cell, which has the zinc plate standing in zinc sulphate 
solution and the copper plate in copper sulphate solution 
and the two solutions separated by a po- 
rous cup as shown in Fig. 33. (Fill the 
porous cup nearly full of zinc sulphate 
solution and allow it to stand three or 
four minutes so that the solution fills the 
pores of the cup and so lets the electricity 
pass through it easily.) Repeat the ex- 
periment of IV and record the behavior of 
this two-fluid cell. Can the Daniell cell 
be called a non-polarizing cell ? Lift up the copper plate 
and examine its surface. Does the fact that copper instead 
of hydrogen has been deposited on the copper plate account 
for the steadiness of the current of the Daniell cell ? 



-r 

mGu 



ZriSOi CxiSOi 
[Porous cup _ 



Fig. 33 



60 LABORATORY MANUAL 

VI. Sal-ammoniac Cell. If time permits, repeat the ex- 
periment of IV using a commercial sal-ammoniac cell (zinc 
and carbon). Does this cell recover after being short-cir- 
cuited ? Break the circuit entirely for a few minutes and 
then connect and read the deflection. 

Question. What kind of cell would you use to operate an 
ordinary electric bell ? Why ? 



EXPERIMENT 30 

MAGNETIC EFFECT OF A CURRENT 

What is the direction of the magnetic lines of force about a wire 

carrying an electric current? 
What is the direction of the magnetic lines of force about a coil 

carrying an electric current? 
How is the distribution of magnetic flux passing through a coil 

changed by inserting a soft iron core? 
How should the windings of an electromagnet be connected? 

Dry cell. Compass (2.5 cm. needle). 

Reversing switch (or commutator). Soft iron rod or core. 
Connecting wires. U-shaped iron core. 

I. Magnetic Field about a Wire Carrying Current. Assum- 
ing that the N-pole of the magnetic needle points in the 
direction of the magnetic lines of force and that the direction 
in which the electricity flows through a zinc-copper (or zinc- 
carbon) cell is from zinc to copper (or carbon) inside the liquid 
said from copper to zinc in the external circuit, we will inves- 
tigate the magnetic field around a wire carrying a current. 

(<z) Connect a simple cell, such as a dry cell, to a revers- 
ing switch (Fig. 34) or commutator (Fig. 35) and then lead 



MAGNETIC EFFECT OF A CURRENT 



61 



the current from south to north 
over a compass. Close the 
circuit by closing the switch 
(or commutator) and record 
the deflection. 

(J) Turn the switch so as 
to reverse the current, caus- 
ing it to flow from north to 
south over the compass. Record the deflection. 

Compare these results with what might be expected from 
the so-called thumb rule. 

If one grasps the ivire with the right hand so that the thumb 
points in the direction of the current, the fingers will point in 
the direction of the magnetic field. 





Fig. 35 



(<?) Put the wire under the compass and without chang- 
ing the direction of the current note the direction of the 
deflection. 

(c?) Pass the current froni the cell over the compass from 
south to north, holding the wire close to the face of the com- 
pass and make the return wire pass under the compass so 
that a loop is made around the compass. Is the deflection 
greater or less than in (a) ? Why? 

II. Magnetic Field about a Coil Carrying Current, (a) Loop 
the wire used in I (d) several times around the compass in 
such a way that the plane of the coil is north and south. 




62 LABOEATOBY MANUAL 

What change in the deflection is produced by increasing the 
number of turns in the coil ? 

(6) Make a helix (Fig. 36) by wrapping the wire say 
fifty times around a lead pencil. Connect this to the switch 

or commutator as in I, 
and see whether or not 
such a helix carrying a 
current acts as a mag- 
*" net with one end at- 
tracting the north pole of the compass and the other repell- 
ing it. Reverse the current through the helix by means of 
the commutator and record the effect that is produced upon 
the poles. 

Compare these results with what might be expected from 
the thumb rule for a coil. 

Grrasp the coil with the right hand so that the fingers point in 
the direction of the current in the coil, and the thumb will point 
to the north pole of the coil. 

- (<?) Make an electromagnet by putting a large iron nail 
or bolt inside the helix. Does this iron core make the poles 
stronger or weaker than before ? How do you know ? 

(d!) Wind the two sides of the U-shaped piece of iron 
with a wire carrying a current, in such a way that one end 
which has been already marked shall be an N-pole and the 
other an S-pole. 

Test the polarity of this horseshoe with a compass. 

In recording the results of these experiments make very 
simple but clear diagrams, showing the polarity and the 
direction of the current in each case. 

Question. An ordinary twisted lamp cord, connected to a 
lighted electric reading lamp, passes over a pocket compass. 
What effect will the current have on the magnetic needle ? 



ELECTBOMOTIVE FORCE 



63 



EXPERIMENT 31 



ELECTROMOTIVE FORCE 

How does the JE. M. F. of a cell depend upon the size and 
character of the electrodes and on the solution or electrolyte ? 

How does the JE. M. F. of a group of cells depend on their 
arrangement (series and parallel) ? 



D'Arsonval galvanometer and 
high resistance coil (1000 
ohms), or voltmeter (0-5). 

Simple voltaic cell (Exp. 29). 

Carbon rod or plate for cell. 

Lead rod or plate for cell. 



Sulphuric acid (1 :20). 
Hydrochloric acid dil. 
Brine, solution of common salt. 
2 Dry cells. 
Connecting wires. 
Connectors for joining wires. 



In order to compare the electromotive 
forces, or the electric pressures of cells, we 
may compare the currents which they 
send through a high resistance galva- 
nometer. A very convenient galvanom- 
eter for this purpose is the d'Arsonval 
galvanometer (Fig. 37), which consists 
essentially of a horseshoe steel magnet 
with a coil of many turns of fine copper 
wire hung between the poles. The coil 
is suspended so that the plane of the coil 
is parallel to the line joining the poles, 
but when a current, even a very slight 
current, is sent through the coil, it is 
turned because it acts as an electro- 
magnet and its poles are attracted and 
repelled by the poles of the horseshoe 
magnet. In this experiment we shall 
connect in series with the galvanometer 




JFig. 37 



64 



LABORATORY MANUAL 




a coil of small German silver wire having 
a resistance of about 1000 ohms. Such 
a galvanometer may be replaced by the 
more convenient voltmeter (Fig. 38), 
which is simply a portable d'Arsonval 
galvanometer with a high resistance coil 
in series. 



Fig. 38 



I. Effect of Size of Cell on the E. M. F. 

Connect a simple cell, such as used in Exp. 29, with the gal- 
vanometer having the high resistance in series. Note the 
deflection of the needle which is attached to the mov- 
able coil. Then move the plates as far apart as possible in 
the jar and again note and record the deflection. Finally 
lift the plates almost out of the liquids and record the 
deflection. 

What effect does the distance between the plates and the area 
of the plates immersed seem to have on the electromotive force of 
a cell ? 

II. Effect of Using Different Metals on the E. M. F. Note 
the direction and amount of the deflection caused by the 
zinc-copper cell. Remove the copper plate and insert a 
carbon plate or rod and again note the direction and amount 
of the deflection. If the deflection is in the same direction 
as above, it shows that the carbon is positive ( + ) with 
respect to zinc ; but if it is in the opposite direction, then 
the zinc is positive ( + ) with respect to the carbon. In the 
same way test the following pairs of metals as electrodes : 
zinc-lead, lead-copper, and lead-carbon. 

Which pair gives the highest E. M. F. ? 

Is there any metal among those investigated that is jyosi- 
tive ivith respect to some metals and negative with respect to 
others ? 



ELECTROMOTIVE FORGE 65 

III. Effect of Different Liquids (Electrolytes) on the E. M. F. 

Note again the amount and direction of the deflection when 
zinc and copper are immersed (a) in dilute sulphuric acid ; 
(6) in dilute hydrochloric acid (HC1) ; (#) in a solution of 
common salt (NaCl) ; (c?) in water (H 2 0). 

The plates should be thoroughly rinsed off before placing 
them in a new liquid. 

What is the effect of the different liquids used as electrolytes 
on the F. M. F. of the cell? 

IV. Effect of Series and Parallel Arrangement on the E. M. F. 

Using the high resistance coil in series with the galvanometer, 
connect two similar cells (such as dry cells) in series, that 
is, connect the zinc of 
one to the copper (or /^g\^^ g \ + 



W V_^ 




carbon) of the other as 

shown in Fig. 39 and 

record the deflection. FlG " 39 FlG ' 40 

Then connect the same cells in parallel, that is, zinc to zinc 

and copper to copper, as shown in Fig. 40, and again read 

and record the deflection. 

Compare these results with the deflection of a single cell. 

What is the effect of the series arrangement on the F. M. F? 
What is the effect of the parallel arrangement on the FJ. M, F? 

Question. Six storage cells, 2 volts each, are connected in 
two rows of three cells each. The three cells in each row 
are joined in series, and two rows of cells are joined in 
parallel. What is the E. M. F. of this arrangement ? 



66 LABORATORY MANUAL 

EXPERIMENT 32 

THE FALL OF POTENTIAL ALONG A CONDUCTOR 

When a steady current is flowing along a conductor, how does 
the fall of potential (" voltage ") between two points vary with 
the resistance? 

When the resistance remains fixed, how does the fall of potential 
depend upon the current ? 

Low resistance galvanometer Voltmeter (low range) or 

or ammeter (0-5 amp.). high resistance galva- 

1-meter high-resistance wire nometer. 

stretched along a meter stick. Variable rheostat. 

Storage battery (3 cells) or 
other source of steady cur- 
rent, such as Daniell cells. 

I. Potential Difference across Equal Resistances. Connect 
one meter of high resistance wire in series with a low reading 
ammeter (A), an adjustable resistance (B), and a source of 
steady current, such as a battery of storage or Daniell cells 
(Fig. 41). Make the connections such that the current enters 




Fig. 41 



at the end marked and adjust the resistance so that the cur- 
rent is one ampere. Touch the + terminal of a low reading 
voltmeter (F) to the terminal of the wire and touch the 
other terminal firmly against the wire at a point just 10 cm. 
from the terminal. Read carefully the voltmeter and 
record this as the potential difference or difference in electrical pres- 



THE FALL OF POTENTIAL ALONG A CONDUCTOR 67 

sure between the ends of this 10-em. length of wire. In the 
same way measure the fall of potential (or voltage) from 10 
to 20, 20 to 30, etc., i.e. for each 10-cm. length along the 
wire. Assuming the wire is of uniform cross section, how 
do the resistances of equal lengths compare ? What conclu- 
sion can you draw regarding the drop in potential for equal 
resistances and the same current? 

II. Potential Difference across Varying Resistances. Con- 
nect the + terminal of the voltmeter to the end of the wire 
and place the other terminal successively at 10, 20, 30 cm., 
etc., and record the voltage for each case. How does the 
resistance of 20 cm. of wire compare with the resistance of 
10 cm.? How does the drop in potential (or voltage) across 
20 cm. of wire compare with that across 10 cm.? Compare 
the resistances and voltages for 40 cm. and 80 cm. lengths 
in the same way. 

When the current is constant in a conductor, hoiv does the 
drop in potential depend on the resistance ? 

III. Effect of Varying Current on Potential Difference. 

Measure the voltage across 50 cm. of wire when the current 
is 0.5 ampere and then 1.0, 1.5, 2.0, 2.5, and 3.0 amperes. 

How does the fall of potential in any given conductor vary 
with the current flowing ? 

Upon what does the drop in potential across any given con- 
ductor depend? 

Note. The terms "drop in potential" and "potential difference' ' as 
used in this experiment mean the same thing — " voltage." 

Problem. A generator is sending 7.5 amperes through 
two resistances, 8 ohms and 10 ohms in series. What is the 
voltage across the 8-ohm resistance ? What is the voltage 
across the 10- ohm resistance ? What is the voltage across 
both resistances ? 



68 LABORATORY MANUAL 

EXPERIMENT 33 

DETERMINATION OF RESISTANCE BY USE OF AMMETER 
AND VOLTMETER 

How should the ammeter be used to measure current (a) in two 

coils in series, (b) in two coils in parallel ? 
How should the voltmeter be used to measure the voltage (a) 

across two coils in series, (b) across two coils in parallel ? 
How can we compute the resistance of (a) each of the two coils 

and (b) of the two coils in parallel ? 

110-volt direct current line or Fuses. 

storage battery. Voltmeter (0-150). 

Two resistance coils of manga- Ammeter (0-15). 

nin wire, or la la wire. 

I. Measurement of Current. Join the two coils in series 
and connect with the 110-volt D.C. service or other supply 
of steady current. Place the ammeter (a) between coil 1 
and the power, (5) between coil 1 and coil 2, (c) between 
coil 2 and the power. Record the average reading of the 
ammeter in each position. What do you conclude about the 
current in a series circuit ? Where should the ammeter be 
placed in a series circuit ? 

Join the two coils in parallel and measure the current 
with the ammeter (&) in the line between the coils and the 
power, (J) in the circuit of No. 1 alone, and (#) in the circuit 
of No. 2 alone. Compare the sum of currents in (V) and (c) 
with the current in (a). Where must the ammeter be placed 
to measure the current in a branch circuit ? 

II. Measurement of Voltage. With the coils in series, 
measure the voltage across (a) the two coils together and 
(6) each coil alone. Take the average reading of the volt- 



DETERMINATION OF RESISTANCE 69 

meter. Compare the sum in (6) with the reading in (a). 
What is the effect upon the current flowing through each 
part of a series circuit, if the resistance of any unit is de- 
creased ? 

Connect the two coils in parallel and take the voltage be- 
tween the binding posts of each coil. Compare these read- 
ings. Assuming a constant voltage service, what will be the 
effect upon the voltage across the group if the resistance of 
one coil is decreased ? Upon the current flowing along that 
coil ? Upon the current in the other coil ? In the line ? 

III. Computation of Resistance. From the readings in 
Part I and II, compute, using Ohm's Law, the resistance of 
each coil and the joint resistance of the two coils in paral- 
lel. Compare this latter result with that obtained by com- 
puting the joint resistance from the separate resistances. 
In recording the data of this experiment, make careful dia- 
grams to show the connections. 

Problem. A circuit has two branches, one of 2 ohms, the 
other of 12 ohms. The current in the 2-ohm branch is 5 
amperes. What difference of potential is maintained between 
the terminals of the circuit ? What current flows in the 
second branch ? 



70 LABORATORY MANUAL 



EXPERIMENT 34 

MEASUREMENT OF RESISTANCE BY WHEATSTONE 

BRIDGE 

How can resistances be compared by a Wheatstone bridge ? 
What is the resistance of 50 ft. of No. 30 copper wire? 

2 dry cells. D'Arsonval galvanometer. 

Key. Resistance box or known resistance coils. 

Wheatstone bridge. 50-f t. coil of No. 30 copper wire. 

The Wheatstone bridge consists essentially of a loop of 
four resistances, indicated in Fig. 42 as R, X, w, and n. 

When the key, if, is closed, the 
current from the cells flows into 
the loop at A, and there divides 
so that part (ij) goes through 
AC and part (Jg) through AD. 
A sensitive galvanometer (6r) is 
connected between O and D. 
Then the resistances R, X, ra, 

Fig 42 

and n are so adjusted that no 
current flows through the galvanometer, which means that 
all of I x has to go on through CB and all of I 2 through DJS, 
and also that C and D are " equipotential " points. When this 
adjustment has been made, 

the voltage drop across A O = I X R, 

and the voltage drop across AD = I 2 m. 

But since and D are at the same potential, these voltage 
drops are equal, and j j> _. j r-\\ 

For similar reasons I X X = I 2 n. (2) 




MEASUREMENT OF RESISTANCE 71 

Dividing equation (1) by equation (2), we have 

R_m 
X~~n' 

From this fundamental equation of the Wheatstone bridge, 
if we know i?, ra, and n, we can compute X. 

In the form of this appa- R 

ratus shown in Fig. 43, the 
resistance ABB consists of 




a wire of uniform cross sec- ^r u * j 

tion and one meter long. 

Since the resistances m and 

n are then directly proportional to the distances AB and 

BB, the equation becomes 

R ___ Distance AD 
X~ Distance DB' 

where R is a known resistance such as a resistance box, and 
the distances AB and BB are read off on a meter stick. It 
will be helpful to remember that 

Left Resistance __ Left Distance 
Right Resistance Right Distance m 

Connect the apparatus, as shown in Fig. 43, using a 
50-ft. coil of No. 30 copper wire in position marked X. 
When the key in the battery circuit is closed, the current 
comes to A where it divides, part going through the known 
resistance J2, along the bar of the bridge (whose resistance 
is negligible), and through the unknown coil X to B\ 
the other part going by way of the German silver wire ABB 
to B. If the known resistance is made in the form of a 
resistance box, we may remove the 10-ohm plug, place the 
slider B connected to the galvanometer in the middle of 
the German silver wire, and make contact for an instant 



72 LABORATORY MANUAL 

only. If the galvanometer needle moves, it shows that the 
two points and D are at different potentials. First try 
another value for R, say 1 ohm, and if the galvanometer 
needle swings the other way when contact is made at D, it 
shows that X, the unknown resistance, lies between 1 and 10 
ohms. By trial just as in weighing make a balance between 
R and X. When it is approximately balanced, make the 
fine adjustment by sliding D back and forth along the wire 
until the galvanometer shows no current flowing when the 
contact is made at D. From the above equation compute the 
resistance of 50 ft. of No. 30 copper wire. 

Repeat the experiment twice, using slightly different 
values for i?, the known resistance. Find the average or 
mean value of these three results and compute from this the 
resistance of 1000 feet of No. 30 copper wire. Compare this 
with the result given in the Wire Tables in the Appendix. 

Problem. In testing a certain Wheatstone bridge, a 
standard 5-ohm coil is placed at R and a standard 4-ohm 
coil at X. What is the correct position of D, i.e. what are 
the correct values for m and n ? 



INTERNAL RESISTANCE OF A BATTERY 73 

EXPERIMENT 35 

INTERNAL RESISTANCE OF A BATTERY 

What is the effect on the current of decreasing the size of the 
plates of a cell and the distance between them ? 

When the external resistance is small, what effect does it have 
on the current to arrange cells (a) in series and (b) in 
parallel? 

How can we measure the internal resistance of a cell? 

Daniell cell. Two dry cells. 

Ammeter or low resistance gal- High resistance wire such as 

vanometer. No. 36 G. S. wire. 

In this experiment we shall consider only cases where the 
external resistance is small. To measure the current we 
shall use an ammeter or galvanometer with low resistance. 

I. Effect of Internal Resistance on Current Furnished by a 
Cell. Connect a Daniell cell to an ammeter and observe the 
effect of bringing the zinc and copper plates (a) near together 
and (b) far apart. What effect on the internal resistance of 
a cell does it have to increase the distance between the 
plates ? 

Gradually lift the plates out of the liquid and record the 
effect on the current. What effect on the internal resistance 
of a cell does it have to diminish the area plates immersed ? 

II. When the External Resistance is Small, what Combina- 
tion of Cells gives the Greatest Current ? (a) Connect two 
similar cells in series with an ammeter and record the cur- 
rent. Compare this with the current furnished by one cell. 
How do the results of this experiment compare with results 
of testing the E. M. F. of two cells in series (Exp. 31) ? 



74 LABORATOBY MANUAL 

(5) Join two cells in parallel and observe the current. 
Compare this with the current strength of one cell. How 
do these results compare with the E. M. F. test of two 
cells in parallel ? How do you explain this difference ? 

III. Measurement of Internal Resistance. Connect a 
Daniell cell with an ammeter and record the current. In- 
troduce into the circuit some high resistance wire, such as 
No. 36 German silver wire, sufficient to reduce the current 
to just one half its former value. Measure the length of 
the German silver wire used and calculate from the specific 
resistance of the wire the resistance thus introduced. As- 
suming the E. M. F. of the cell to have remained constant, 
in order to reduce the current to one half, the resistance 
must have been doubled. This means that the internal 
resistance of the cell is equal to the resistance of the Ger- 
man silver wire which has been inserted. 

The internal resistance of cells arranged in series or in 
parallel can be computed just like the resistance of several 
wires in series or in parallel ; that is, the series arrange- 
ment multiplies the internal resistance and the parallel 
arrangement divides the internal resistance of one cell by 
the number of cells. 

How should cells be connected to get a large current when 
the external resistance is small ? When the external resistance 
is large ? 

Problem. A telegraph sounder has a resistance of 70 ohms 
and requires 0.2 ampere to work it. How many gravity 
cells, each of 1.1 volts and 3.0 ohms, will be required? 



MEASUREMENT OF CURRENT 



75 



EXPERIMENT 36 

MEASUREMENT OF CURRENT BY A COPPER 
COULOMBMETER 

How may an ammeter be cheeked by the weight of copper de- 
posited in a certain time ? 



Copper coulombmeter. 

Copper sulphate (CuS0 4 ) 
solution with a little sul- 
phuric acid and alcohol. 

Ammeter. 

Adjustable resistance. 



Watch or clock with second 

hand. 
Beam balance and weights. 
Storage battery or supply of 

steady current. 



The copper coulombmeter consists of a glass jar with two 
anode plates (J., A) and one cathode ( (7) or gain plate placed 
between them (Fig. 44). About 50 
cm. 2 of cathode surface is allowed 
for each ampere of current, and the 
liquid is a solution of copper sulphate 
(CuS0 4 ), slightly acidulated with sul- 
phuric acid (H 2 S0 4 ) and containing 
a little alcohol. The gain plate (cath- 
ode) is first made perfectly clean by 
rubbing with fine emery until bright, 
and then wiping with a clean dry 
cloth. After it is cleaned, the part 
which is to be immersed must not be 
touched by the fingers. 

Weigh this clean cathode as accu- 
rately as you can and set it aside. 

Connect the ammeter to be checked 
with an adjustable resistance in circuit with the coulomb- 
meter and some supply of steady current such as a storage 




—J Cathode [ 



Fig. 44 




Cs 




76 LABORATORY MANUAL 

battery. Insert in the coulombmeter a trial cathode plate, 
not the clean one, but the same size as the one to be used. 
The current must be made to enter at the outside plates 
(anodes) and emerge at the middle or gain plate (cathode) 
(Fig. 45). Close the circuit and adjust 

1 J I u I q the resistance to give the desired current 

(from 1 to 2 amperes). 

Open the circuit and replace the trial 
cathode by the clean weighed cathode 
and again close the circuit, noting ex- 
actly the time (hr. min. sec). Record 
the ammeter reading every ten minutes 
and keep the current constant. After 
30 or 40 minutes, break the circuit and at once remove the 
gain plate. Note the deposit of copper. Rinse off in clean 
water and then in alcohol and dry quickly. Reweigh and 
determine the gain as precisely as possible. 

Compute the gain in weight per hour. 

Assuming that 1.186 g. of copper is deposited by one 
ampere in one hour, compute the average current. 

Compare this value of the current with the average reading 
of the ammeter. 

Problem. How many ounces of copper would be deposited 
from a solution of copper sulphate in 10 hours by a current 
of 2.5 amperes? 



INDUCED CURRENTS 77 

EXPERIMENT 37 

INDUCED CURRENTS 

How may currents be induced by means of a magnet? 
How may currents be induced by an electromagnet ? 
How may a conductor be moved in a magnetic field to generate 
a current? 

D'Arsonval galvanometer. Bar magnet. 

2 dry cells. Soft iron core. 

2 coils of about 800 turns No. Reversing switch. 

28 copper wire. U-shaped steel magnet. 

I. Induction by a Magnet. To see which way the needle 
of the d'Arsonval galvanometer turns when the current 
enters at the right-hand binding post, we may short-circuit 
the instrument with a stout copper wire and connect with a 
simple cell so that the current enters at the right terminal 
of the galvanometer. Place a piece of paper near the in- 
strument and record the direction of the deflection with an 
arrow when the right terminal is made positive ( + ). Con- 
nect to the galvanometer (now without any shunt) a coil of 
many turns (say 800 turns of No. 28 
copper wire). 

(a) Now move the coil downward 
quickly over the N-pole of the bar 
magnet (Fig. 46), and record the 
direction and amount of the deflec- 
tion. From this deflection, deter- 
mine the direction of the current 
induced in the coil. While this current was flowing in the 
coil, it made the coil a temporary magnet. What was the 
polarity of the side of the coil approaching the N-pole of 
the magnet ? 




Fig. 46 



78 LABORATORY MANUAL 

(h) Quickly remove the coil from the magnet and record 
the direction and amount of the deflection. Compare the 
direction and amount of the current thus induced with that 
in part (a). What is the polarity of the end of the coil 
that last leaves the magnet's N-pole ? 

(tf) Repeat (a) and (5) using the S-pole of the magnet 
and in each case determine the direction of the current in- 
duced in the coil. Is the direction of the induced current such 
as to oppose or to assist the motion of the coil ? 

II. Induction by an Electromagnet. Insert an iron rod 
in a coil S which is connected to the galvanometer. Con- 
nect through a commutator one or two dry cells to a similar 
coil P which is placed on the iron rod beside coil S. 

(a) Now close the circuit by the commutator or switch 
and record the deflection of the galvanometer. From this 
determine the direction of the current induced in the coil S. 
Was this current induced in coil S (called the secondary) 
in the same direction as the current in coil P (called the 
primary) ? Explain how this might be expected from the 
experiment in Part I. 

(5) Break the circuit at the commutator and note direc- 
tion and amount of the deflection. Compare this with that 
induced when the circuit is closed. 

Is the induced current in the same or in the opposite direc- 
tion to that which is flowing in the primary coil ? Note that 
the current is induced by the changes in the magnetism of 
the electromagnet. Is the direction of the induced current 
such as to oppose or assist the changes in the magnetism of the 
iron core ? 

III. A Current Generated by Moving a Conductor across a 
Magnetic Field. Hold the coil S which is connected to the 
galvanometer between the poles of a horseshoe magnet in 



EFFICIENCY OF AN ELECTBIC MOTOR 



79 



Galv. 




K\ 



x 



such a way that the plane of the coil is at right angles to 
the line joining the poles (Fig. 47). Quickly turn the coil 
a quarter turn so that the plane of the 
coil is parallel to the magnetic field. 
Observe the direction of the induced 
current. After the galvanometer has 
come back to zero, rotate the coil an- 
other quarter turn and note the di- 
rection of the induced current. In a 
similar manner continue to rotate the 
coil one quarter turn at a time. In 
what position is the coil when the in- 
duced current is reversed? Fig. 47 

Note. In this experiment it will be helpful to record the results in the 
form of very simple sketches showing the direction of the motion and induced 
current and polarity of the magnet. 

Question. A coil is rotated in a magnetic field in such a 
way that no current is induced. What is the direction of 
its axis of rotation ? 




EXPERIMENT 38 



EFFICIENCY OF AN ELECTRIC MOTOR 

What is the ratio of the mechanical output of an electric motor 
to the electrical input ? 



0.25 horse power motor. 
110- volt direct current 
line or storage battery. 
Ammeter. 
Voltmeter. 



Two spring balances and sup- 
port. 
Cord or strap for brake. 
Speed counter. 
Watch. 



Connect a small D. C. motor to some supply of electric 
current. Insert an ammeter in the line to measure the in- 



80 



LABORATORY MANUAL 




Fig. 48 



tensity of the current /and put a voltmeter across the brushes 
(Fig. 48) to get the electrical pressure E. From these two 

factors we may eas- 
ily compute the input 
in watts which is 
equal to the 'product 
of volts times am- 
peres. 

To get the mechanical output we may make a brake test. 
A very simple form of brake consists of a belt or cord 
attached to two spring balances and passing under a pulley 
on the motor shaft, as shown in Fig. 49. If the motor ro- 
tates clockwise, as indicated, it is 
evident that the spring balance A 
will have to exert more force than 
balance B because of the friction of 
the pulley on the cord. The amount 
of this friction is equal to the differ- 
ence between the readings of A and 
B, and it is exerted each minute 
through a distance equal to the cir- 
cumference of the pulley times the 
revolutions per minute. The work 
done in one minute is equal to the 
friction times the distance per minute. 
First determine the circumference 
of the pulley by measuring the length of fine wire required 
to make one turn around the pulley. To determine the 
number of revolutions per minute, hold a speed counter 
(Fig. 50) against the end of the motor shaft (S) for just 
one minute. 

When all the apparatus is assembled, start the motor by 
closing the switch. Throw on the load by increasing the 




Fig. 49 



EFFICIENCY OF AN ELECTRIC MOTOR 



81 



tension on the brake cord so as to slow down the 
motor a little. Keeping this pull steady, we get 
the speed of the motor and at the same time read 
the spring balances, ammeter and voltmeter. Then 
repeat this experiment, putting more load on the 
motor by pulling more strongly on the balances. 
Finally, make a third trial with still more load on 
the motor. 

It will be convenient to record the data and 
results in tabular form, somewhat as follows : 




Fig. 50 





First Trial 


Second Trial 


Third Trial 


Voltmeter reading 

Ammeter reading 








Watts put in motor 

Number of revolutions per minute . 
Distance meters per minute . . . 
Balance A reading (kg.) .... 
Balance B reading (kg.) .... 








Friction (A - B) (kg.) .... 
Work got out of motor (watts) . . 
Efficiency % 









It will be helpful to know that 1 watt = 6.12 kilogram- 
meters per minute. 

Does the efficiency of the motor change when the load is 
changed? Why does the amount of current supplied to the 
motor change as the brake load increases? 

Problem. At 10 cts. per K.W.-hour, how much will it cost 
per week of 54 hrs. to run a motor, having an average load 
of 10 H.P., and an average efficiency of 90 % ? 



82 



LABORATORY MANUAL 



EXPERIMENT 39 



HEATING EFFECT OF AN ELECTRIC CURRENT 

How many joules of electrical energy are equivalent to one 
calorie of heat ? 



Calorimeter and stirrer. 
32 c.p. lamp and socket. 
Platform scales and weights. 
Thermometer. 
Connecting wires. 



Ammeter. 

Voltmeter. 

Source of current, 110 volt service 

or storage battery. 
Watch or clock with second hand. 



Weigh a calorimeter with its stirrer. Then pour in 
enough water at about 10° C. below the room temperature to 
cover the bulb of a 32 candle power lamp and weigh the 

beaker again to get the weight of 
the water. Insert the lamp bulb 
and a thermometer in the calorim- 
eter ((7) and connect an ammeter 
(J.) in series with the lamp (_L) and a volt- 
meter ( F) in shunt with the lamp as shown 
in the Fig. 51. Stir the water and note its 
temperature and then turn on the current at 
S) noting precisely the time of doing so. 

Allow the water to be heated about as 
much above the room temperature as it 
started below, stirring continually. In the 
meantime read the voltmeter and ammeter 
every two minutes. When the current is 
cut off, note the time and the highest temperature to which 
the water rises. 

Record the data and results in tabular form as follows : 




Fig. 51 



HEATING EFFECT OF AN ELECTRIC CURRENT 



83 



Observations 

Weight of beaker and stirrer . . 
Weight of beaker, stirrer, and water 
Temperature of water at start . 
Time of start (hr. min. sec.) 
Temperature of water at finish 
Time of finish (hr. min. sec.) . 



Volts Amperes 



g- 
g- 

°C. 



Calculated Results 

Weight of water -f water equivalent of calorimeter 

Rise in temperature 

Calories of heat absorbed 

Time of run in seconds 

Average volts 

Average amperes 

Joules (watt-seconds) delivered to lamp . . . . 
Number of joules per calorie 



Problem. Assuming that one joule (watt-second) is 
equivalent to 0.24 calorie, compute the price per calorie for 
the heat generated in an electric iron using 3.5 amperes at 
110 volts. The cost of electricity is 10 cts. per K. W.-hour. 



84 



LABOBATOBT MANUAL 



EXPERIMENT 40 

FREQUENCY OF A TUNING FORK 

How many vibrations does a tuning fork make in one second? 



Bristles or stiff paper points. 

Wax. 

Releasing clamp for tuning 

fork. 
Thin shellac. 



Tuning fork. 

Recording apparatus (Fig. 52). 
Glass plates. 
Stop watch. 

Alcohol lamp filled with tur- 
pentine and alcohol. 

a tuning fork (-F), 
with a fine wire 
or paper point at- 
tached to one prong, 
and a short pen- 
Fig. 52 ^ dulum (M)i which 

rrMsasssss 

hne beneath the Pom » vibrations, so as to 

at right angles to the ,<b rectton ^^ ^ 

make a wa.y curve , on the glass, ana 

'„ nl 'we can easilv connt on the «ff&£ nl^ 
of vibrations of the fork ~ndu« * Z Zber of 

swings of the pendulum, and thus compu 
vibrations of the fork per second. 




FREQUENCY OF A TUNING FORK 85 

Clamp the tuning fork so that its tracing point is only a 
few millimeters from the point of the pendulum. The line 
of these two tracing points should be parallel to the direction 
in which the glass is to move. The tracing points must rest 
lightly on the smoked » ss surface and yet hard enough to 
scratch away the coating. To test this, set the fork and 
pendulum in vibration with the glass at rest. A good way 
to set the fork vibrating is to squeeze the prongs together 
with a little U-shaped metal clamp and then quickly pull the 
clamp off. 

When the apparatus is properly adjusted, start the pendu- 
lum swinging and set the fork vibrating and then draw the 
glass along the track at such a rate as to have at least one 
complete swing of the pendulum recorded on the glass. 
Several sets of tracings may be recorded on the same plate 
by moving it a little sideways, and so bringing a fresh sur- 
face under the tracing points. 

To get the rate of the pendulum, set it swinging and count 
its vibrations for one minute. Compute the number of 
vibrations of the pendulum per second. 

Next count the number of vibrations of the fork correspond- 
ing to a full vibration of the pendulum, i.e. the number of 



fc £> x 

Fig. 53 

vibrations traced by the fork between the points A and C 
(Fig. 53) or between B and D, estimating in every case to 
tenths of a vibration. 

Compute the number of full vibrations made by the fork 
per second. 

Question. In this experiment what is the effect on the 
curve traced if we move the smoked plate more rapidly ? 



86 



LABOBATORY MANUAL 



Note. If the tracings are made on smoked paper, they may easily be 
" fixed " by pouring over the smoked surface a very thin solution of shellac. 
After a few minutes the paper is dry and may be pasted in the notebook as 
a part of the record of the experiment. 

Since smoked glass is always more or less dirty, the glass is sometimes 
covered with a thin coat of whiting in alcohol. 



EXPERIMENT 41 



WAVE-LENGTH OF SOUND 



Sow long is the sound ivave in air emitted by a vibrating tuning 

fork? 
How fast does the sound wave travel in the air of the room ? 



Tuning fork (n = 512). 
Hydrometer jar of water. 
Resonating tube. 



Large flat cork. 
Meter stick. 
Rubber bands. 



Place the resonating tube in the hydrometer jar and pour 
in water so as nearly to fill the jar. Strike one prong of the 
tuning fork on a large cork stopper and 
j i hold the vibrating fork over the open 
end of the tube (Fig. 54). By raising 
the tube slowly out of the water, a point will 
be found where the air-column is of just the 
right length to reinforce the fork. Mark with a 
rubber band around the tube the position of the 
water where the sound was loudest. Then set 
the fork in vibration again and by raising and 
lowering the tube and listening intently, deter- 
mine again as precisely as you can the point 
where the air-column gives the greatest reinforce- 
ment. Measure the length of the air-column. 
In a similar manner find a second position of the water 
surface nearer the bottom of the tube, which also gives rein- 



Fig. 54 



WAVE-LENGTH OF SOUND 87 

forcement to the sound. Measure the length of this air- 
column and record the temperature of the air. 

The length of the short air-column (plus about 0.3 the 
internal diameter of the tube) is equal to one fourth the wave- 
length of the tone of the fork in air. The difference between 
the length of the short and long air-columns is equal to one 
half a wave-length. 

Compute this difference in length between the two air- 
columns and the length of a wave emitted by the fork used. 

Given the frequency of the fork, i.e. the number of vibra- 
tions per second, compute the velocity of sound at the tem- 
perature of the room, using the wave-length just deter- 
mined. 

It is usually stated that the velocity of sound in air is 1087 
feet per second at 0° C. and that it increases about 2 feet per 
second for each degree C. rise. Compare this value with 
the result of your experiment and compute the percentage 
error. 

Problem. What is the pitch of a closed organ pipe 62 cm. 
long on a day when the temperature is 20° C? 



88 LABORATORY MANUAL 

EXPERIMENT 42 

BUNSEN PHOTOMETER 

What is the candle power of a given electric lamp bulb in terms 

of a standard lamp ? 
What is the intensity of a Tungsten lamp ? 
What is the effect on the downward intensity of an electric lamp 

of adding a shade ? 

Bunsen photometer in a dark room or Voltmeter. 

in a light-tight box. Ammeter. 

Three incandescent lamps (one Tung- Shade for electric bulb. 

sten lamp, and one of known candle 

power). 

Set up a Bunsen photometer in a darkened room, as shown 
in Fig. 55. Use a standard 16 candle power bulb (#) 
as a basis for comparison. Insert a rheostat in the power 



* K^l * 



3 B cm- 



I I 



I Eyes \ 



—A cm © 



I I I 



I Eyes \ 
Fig. 55 

circuit so as to bring the standard lamp to its required 
voltage. At the other end of the photometer, about 200 cm. 
from the first lamp, set up another electric lamp (X) which 
is to be tested. Between these two lamps place the sight 
box or screen (6r) with the grease spot. This screen is to 
be moved back and forth between the lights until a position 
is found such that the screen is equally illuminated on both 
sides, that is, such that the central spot or disk and the sur- 
rounding rim of paper are of the same brightness. Since it 



BUNSEN PHOTOMETER 89 

is difficult to set this sight box or screen precisely, several 
trials should be made and the average position taken. 

Suppose that the lamp X to be tested is found to be A cm. 
from the screen and the standard lamp S equally illuminates 
the screen when B cm. away. If the distances A and B are 
equal, then the candle powers of the two lamps are the same; 
but if these distances are not equal, the lamp which is farther 
from the screen has the greater candle power. Further- 
more, since the intensity of illumination decreases as the 
square of the distance, the candle powers of the two lamps are 
directly proportional to the squares of their distances from the 
screen. That is, jr 42 

In this way, knowing S and measuring A and i?, we can 
compute X. Find the candle power of an ordinary electric 
lamp bulb; that is, the mean horizontal candle power. From the 
readings of the voltmeter and ammeter in the lamp circuit, 
compute the cost of maintaining such a lamp for one hour 
and the cost per candle power. 

Similarly, find the candle power of a 50-watt Tungsten 
lamp. 

Finally, turn an incandescent lamp into such a position as 
to measure its candle power downward both with and with- 
out a shade. 

Problem. If a 16 candle power lamp is 85 cm. from a 
Bunsen photometer screen, how far must a 20 candle power 
lamp be on the other side, when the screen is properly 
adjusted ? 



90 LABORATORY MANUAL 

EXPERIMENT 43 

IMAGE IN A PLANE MIRROR 

How does the angle of incidence compare with the angle of 

reflection ? 
How does the image in a plane mirror compare with the object 

in respect to size, distance, and form? 

Plane mirror. Protractor. 

Block for holding mirror with Ruler. 

rubber bands. Block with vertical black line on 

Paper. one face. 

I. Reflection in a Plane Mirror. Draw a straight line 
across a sheet of paper and label this the Mirror Line. Set 
up the mirror so that its reflecting surface is exactly over 
this line. At a distance of 10-15 cm. in front of the mirror, 
make a dot and label it 0. Place the small block with its 
vertical black line standing directly over this dot. To locate 
the image of this line lay a ruler on the paper so that its 
edge points directly at the image. Care should be taken to 
sight with one eye only along the edge of the ruler and 
then draw a clean sharp line along the edge that points 
toward the image. To make sure that the ruler has not 
slipped in this process, remove the ruler and look along the 
surface of the paper and see if the line does really point at 
the image. If not, erase the line and try again. 

Place the ruler on the other side of the small block and 
make another sight line just as before, making sure that the 
mirror still has its reflecting surface just on the mirror line. 

Remove the mirror and block and continue each of the 
sight lines as solid lines up to the mirror line and then con- 
tinue them as dotted lines behind the mirror until they meet. 



IMAGE IN A PLANE MIRROR 



91 



Mark this point of intersection, J, the image-point. The 
solid sight lines represent reflected rays. From the object- 
point, (9, draw lines to the intersection of each of these sight 
lines with the mirror line. These lines from to the mirror 
represent the incident rays. Connect the object-point, 0, with 
the image-point, J, making it solid in front of the mirror and 
dotted behind the mirror. Indicate the direction in which 
light travels along the lines by arrows, as in Fig. 56. 

At one of the points of reflection erect a normal, that is, a 
perpendicular to the mirror, and label the angle between the 
incident ray and this normal the angle of incidence, and the 
angle between the reflected ray and the normal the angle of 
reflection. 

Distance of object from mirror cm. 

Distance of image from mirror cm. 

Angle betv^een 01 and the mirror line ° 

Angle of incidence ° 

Angle of reflection . . ° 

II. Image in a Plane Mirror. On another sheet of paper 
draw a line across the middle and set up the mirror as be- 




A 


B 

> ! 




,'' 




Mirror 






Line 



Fig. 56 



(&) 



fore. Draw an arrow about 5 cm. long and label it AB, as 
shown in Fig. 56. Locate as in I the image-points of A and 
B and label these points A f and 5'.. Construct with a 



92 LABOBATOBY MANUAL 

dotted line the image of AB. Measure the length of A'B f . 
Prolong the lines AB and A! B f until they intersect. Where 
does this point of intersection lie ? The mirror line is called 
in mathematics the axis of symmetry. If the paper is folded 
along the mirror line and if the work has been carefully 
done, the image will be found, when the paper is held to the 
light, to coincide with the object. 

Compare the object with its image in a plane mirror with 
respect to size, distance, and form. 

Question. What is the difference between the image that 
one sees of himself in a plane mirror and the appearance one 
presents to other people ? 



EXPERIMENT 44 

IMAGES IN CYLINDRICAL MIRRORS 

I. What is the position, size, and shape of an image formed 
in a convex mirror ? 

II. What is the position, size, and shape of an image formed 
in a concave mirror? 

Convex-concave cylindrical mirror. Ruler. 

Paper. Pins. 

I. Convex Mirror. Place on a sheet of paper a convex 
cylindrical mirror so that its straight lines are vertical, and 
then trace on the paper the position of its convex surface. 
About 5 cm. in front of the mirror draw as object an arrow 
4 cm. long and label it A, B, 0, as shown in the Fig. 57 a. 
To locate the position of the image of A, place a pin at point 
A so that it stands erect and then draw two sight lines along 
the edge of a ruler (one on each side of the pin) pointing at 



IMAGES IN CYLINDRICAL MIRROBS 



93 



the image of the pin. Label each of these lines A. Then 
stand the pin at B and draw, as before, two sight lines 
toward the image. In the same way draw sight lines to 
locate the image of C. 



A- 
F 
-B 

c 



> Concave 
Mirror 



, Object 



I 



-D 



(a) 



Fig 57 



(&) 



Remove the mirror and pin and continue each pair of sight 
lines until they intersect. In this way locate the image- 
points of A, B, and O and label these points A ', B', C. 
Draw a line from A' through B ! to r with an arrow at A! . 
Label this arrow the Image. 

Compare the object and its image in a convex mirror as to 
position, size, and shape. 

II. Concave Mirror. Stand the mirror a little above the 
middle of a sheet of paper and draw a sharp line along its 
concave edge. Remove the mirror and draw a dotted line 
connecting the ends of the arc. Draw a perpendicular at 
the mid-point of this chord and label it axis. Assuming that 
the radius of curvature is 5 cm., mark the center of curvature 
with the letter (7. Mark the focus F, which is halfway 
between the center of curvature and the mirror M, as 
shown in Fig. 576. In order to locate the images of objects 




94 LABORATORY MANUAL 

at varying positions along the axis, draw a short arrow 
between F and M and label it A, another between F and O 
and label it B, and a third beyond and label it D, some- 
what as shown in the figure. 

Replace the mirror on its line and observe the direction, 
curvature, and relative length of the images of A and B. In 
order to see these images more distinctly, it will be useful to 
draw an arrow on a small strip of paper and fold up one end 
so that the arrow is on the vertical part as shown in Fig. 58, 

and then place this strip of paper 
over A and B. Do the images of 
A and B point in the same direc- 
tion as the objects ? 

To locate the position of the 
image of A, stand a pin upright at the mid-point of A 
and draw two sight lines directly at its image. Label these 
lines A, A. Locate the images of B and Q in the same 
way. 

When an image seems to be back of a mirror, it is said to 
be virtual, because the rays of light do not actually come 
from the image-point but simply look as if they had come 
from it. On the other hand, when as in some cases with a 
concave mirror the image is found in front of the mirror, it 
is said to be a real image because the rays actually do pass 
through the image-point. 

State where the object must be placed in order to get a virtual 
image and where to get a real image. 

State where the object must be placed in order to get an image 
pointing in the same direction as the object and where to get a 
reversed image. 

State where the object must be placed in order to get an image 
which is smaller than the object and where to get a larger 
image. 



INDEX OF REFBACTION OF GLASS 



95 



Question. What would one observe if he stood at first 
close in front of a concave mirror and then gradually moved 
away from it ? 

EXPERIMENT 45 



INDEX OF REFRACTION OF GLASS 

What is the relation between the speed of light in air and in 

glass f 



Rectangular glass plate. 

Paper. 

Ruler. 



Protractor. 

Pins. 

Millimeter paper scale. 



Lay a rectangular glass plate on a sheet of paper in the 
position shown in Fig. 59 and trace with a sharp pencil the 
edge of the glass. Stand a pin upright at A, touching the 
edge of the glass. 





Fig. 59 



If one places one's eye on a level with the paper and looks 
into the edge DE, the portion of the pin A seen through the 
glass seems to be in line with the part seen over the glass 
only when the eye looks into the glass in the direction FD, 
perpendicular to the edge DJE. 

In order to show just how much a ray of light is bent in 
passing from glass to air, place a second pin B close to the 



96 LABORATORY MANUAL 

edge BE as shown in the figure. Now move the head 
slowly to the left until the pin B just covers the image of 
pin A seen through the glass* Place a ruler so that one edge 
points directly at B and the image of A seen through the 
glass, and then draw the sight line G. 

Remove the glass, and connect the points A and B, which 
line represents the direction of a ray of light through the 
glass. Prolong the sight line until it strikes the point B. 
This sight line shows the direction of the ray AB after leav- 
ing the glass. 

The refraction of light in passing from glass into air de- 
pends on the relative speeds of light in glass and air. If we 
erect a normal MN at B perpendicular to DE, we find that 
the angle in air is greater than the angle in glass. It has also 
been found that the speed of light in air is to the speed in glass 
as the sine of the angle in air is to the sine of the angle in glass. 
To get this ratio of the sines of these angles, lay off on AB and 
BO equal distances (the longer the better), such as BE and 
BGr, and draw FH and GK perpendicular to the normal MN. 
The sine of angle a is GK/B G and the sine of angle b is 
EH I BE, but since BF=BG, 

sine Aa __ GK 
sine Z.b~~ ~EH 

In short, to get the index of refraction of the glass used in 
this experiment, i.e. ratio of speed of light in air to speed of 
light in glass, we have merely to divide the length of GK 
(measured to tenths of a millimeter) by the length of EH. 

To make a second trial, move the position of pin A to a 
new point A! along the edge of the glass and repeat the 
experiment. 

Question. The index of refraction of water is 1.33. Does 
this mean that water refracts light more or less than glass ? 



FOCAL LENGTH AND CONJUGATE FOCI 97 



EXPERIMENT 46 

FOCAL LENGTH AND CONJUGATE FOCI OF A CONVERG- 
ING LENS 

How far is the picture of a distant object from a convex lens? 
What relation exists between the object-distance and the image- 
distance when the object is near a convex lens? 

Optical bench (Fig. 60) White cardboard screen. 

(meter stick and supports). Holders for lens and screen. 

Screen with wire netting. Electric or gas lamp. 
Double convex lens (f. 10-15 cm.). 

I. Focal Length. An object which is 100 feet or more 
away sends to a lens rays that are practically parallel, i.e. 
rays from any distant object-point to different parts of the 
lens are very nearly parallel. These parallel rays converge 
at a point called the principal focus and the distance between 
the lens and the principal focus is called the focal length. 

Set the double convex lens and the cardboard screen on a 
simple optical bench (Fig. 60) and hold the bench in the 





o ' ; ' ' ' 40 ' ! ! 'so 60 " : . ' jo ■ : = j^ ' ; 106] 

' ^ *-unuJ 

Fig. 60 

back part of the room but pointing at some distant object 
out of the window. Having placed the lens on one of the 
main divisions of the meter stick, move the screen toward 
and away from the lens until the most distant bright object 
which can be seen through the window is sharply focused 
on the screen, i.e. forms a clear picture. Read and record 
the positions of lens and screen. 



98 



LABORATORY MANUAL 



Move the lens to a new position on the stick, and again 
make a new setting of the screen in the same way as before. 
After making a third trial, find the average of the three 
focal lengths and record this as the focal length of the lens. 

II. Relations of Object and Image. Set up the optical 
bench as shown in Fig. 60, so that the object (an illuminated 
wire netting) is away from the window. Place the card- 
board screen at the opposite end and darken the room. Slide 
the lens back and forth between this screen and the object 
until a position is found where the picture of the netting 
appears on the screen as sharp as possible. 

Is the image larger or smaller than the object ? 

Cover one part of the object and see if the image is erect or 
inverted. 

Without moving the object or the screen, try to find 
another position of the lens that will give a sharp image. 

Is it smaller or larger than the object, erect or inverted? 

When the image is smaller than the object, which is nearer 
the lens, the object or the image ? 

When the image is larger than the object, which is nearer the 
lens, the object or the image ? 

Read the position of the object, lens, and image on the 
meter stick as accurately as possible, and record in tabular 
form as follows : 





Positions 


Object- 
distance 


Image- 
distance 


1 , 1 


1 


Object 


Lens 


Image 


Obj.-dist. "*" Im.-dist. 


Focal Length 

















SIZE AND SHAPE OF A REAL IMAGE 99 

Move the screen up nearer the object and again find two 
positions where the lens forms a sharp image. 

Continue to move the screen up closer to the object until 
it is possible to get only one distinct image. What is the 
shortest distance between object and screen, at which the lens 
will form a distinct image ? How many times the focal length 
of the lens is this minimum distance between object and image ? 

Compare the sum of the reciprocals of the image- and object- 
distances with the reciprocal of the focal length. 

Problem. What is the focal length of a lens if the image 
of an object 10 ft. away is 5 in. from the lens ? 



EXPERIMENT 47 

SIZE AND SHAPE OF A REAL IMAGE 

Is the real image of a straight line formed by a convex lens 
straight or curved ; and if curved, does its center bend toward 
or away from the lens? 

How are the image- distance, object-distance, length of image, 
and length of object related ? 

Strip of paper (about 20 x 75 cm.) . Block with vertical line. 

Meter stick. Block with bent wire. 

Double convex lens and holder. 

Lay a strip of paper on the table so that the long side 
extends toward the window. Draw a line down the middle 
of the paper and near the end farthest from the window, 
draw an arrow about 10 cm. long. Divide the arrow into 
four equal parts and mark the points of division 1, 2, 3, 4, 
and 5 as shown in Fig. 61. On the long line, mark the 
position of the lens, which should be distant from point 3 of 




100 LABORATORY MANUAL 

the arrow from one and a half to two times the focal length 
of the lens ; that is, if the lens has a focal length of 12 cm., 
place it from 18 to 24 cm. from the center of the arrow. 

it— 

Fig. 61 % 

Place the lens so that its center is directly over this point 
and its plane at right angles to the line. To locate the 
image-points corresponding to each of the five points of the 
object, stand the vertical line of the wooden block directly 
over point 3, and using one eye only, look into the lens from 
the other end of the paper so as to see the image of the ver- 
tical line. Move the block carrying the bent wire until the 
vertical part of the wire just covers the image. To see the 
wire and image distinctly, the eye should be about 30 cm. 
away from the wire. Move the wire to and from the lens 
until a position is found where, as the head moves slowly 
from side to side, the wire and the image keep exactly to- 
gether, showing that each is at the same distance from the 
eye. As soon as this position is sharply determined, mark 
a dot directly under the point of the wire and label it 3'. 

Move the vertical line along to 4 and locate in the same 
way the position of its image 4'. In this manner determine 
the position of the image of each of the five points of the 
object arrow. In locating these points it is quite essential 
that the observer should not let any preconceived notion as to 
the proper position of the image-points affect his judgment 
as to where each image-point really is. 

Connect the image-points l'and 2' and 3', etc., with straight 
lines to get a rough idea of the shape of the whole image. 
Draw a straight line from each object-point to its corre- 
sponding image-point. Where do these lines intersect? 



SIZE AND SHAPE OF A EEAL IMAGE 101 

Connect the ends of the image arrow by a straight line, 
measure its length, and call it L { . Measure the distance of 
the lens from the center of the object and the distance of 
the lens from the point where the straight line joining the 
ends of the image crosses the axis, and call these distances 
D and D t respectively. 

Call the length of the object X , compute the value of the 

ratio — £ which is called the magnifying power of the lens. 

D 

Also compute the value of the ratio —± and compare this 

result with the magnifying power. (Express the ratio to 
three significant figures.) 

Does the center of the image bend toward the lens or aivay 
from it? 

To explain this curvature of the image consider D for 
point 1 and D for point 3. Then, if the lens formula 

( — + — = -] holds true, and / is a constant for the lens, 

what would be expected of Di for point 1 and D { for 
point 3? 

Sow is this defect in a lens corrected so as to give what the 
photographers call a "flat image " ? 

Problem. A lantern slide picture 3 inches long is to be 
projected on a screen 30 feet away so as to form a picture 
6 feet long. What must be the focal length of the lens ? 
How far from the slide must the lens be placed? 



102 LABORATORY MANUAL 

EXPERIMENT 48 

MAGNIFYING POWER OF A SIMPLE LENS 

How many diameters does a converging lens seem to magnify an 

object ? 

Meter stick. Paper millimeter scale. 

Double convex lens (f. 2.5-7.5 cm.) Black cardboard with square 
and holder. hole and holder. 

In many optical instruments a double convex lens is used 
as a simple microscope or magnifying glass. For the aver- 
age person the distance of most distinct vision is about 
25 cm. (10 in.), but with a magnifying glass, the distance 
between the lens and the object is made a little less than 
the focal length and so adjusted that an erect enlarged 
virtual image is formed about 25 cm. away. To get the 
magnifying power of a simple microscope we have to find 
the ratio of the size of the image to the size of the object. 
This is, however, equal to the distance of the image divided 
by the distance of the object, that is, 25 /D where D is the 
object-distance in centimeters. 

First find the focal length of the lens by holding a meter 
stick horizontally with one end against a piece of white card- 
board and with the other end pointing at some distant object 
outside the window. Hold the lens in the hand and move 
it slowly away from the screen until it forms a clear picture. 
This distance between the lens and the screen is the focal 
length of the lens. Record the focal length and number of 
the lens. 

Place a paper millimeter scale on the table and stand a 
meter stick upright on it. At a distance of 25 cm. fasten a 
short focus lens to the meter stick. Then just under the 



MAGNIFYING POWER OF A SIMPLE LENS 



103 



\Lens 



Screen 



I 



lens set a black cardboard screen with 
a square opening (1 cm. 2 ) at a distance a 
little less than the focal length of the 
lens, as shown in Fig. 62. Bring the head 
down so that the right eye is directly over 
the lens and adjust the screen so as to 
get a sharp image of its surface. Keep- 
ing both eyes open, count the number of 
millimeters which the image of the open- 
ing in the cardboard, as seen by the right 
eye through the lens, seems to correspond 
to on the millimeter scale as seen by the 
unaided left eye. Divide this number by 
the width (10 mm.) of the opening in the 
cardboard and the quotient gives how 
many times the object seems to be mag- 
nified when seen through the lens as 
compared to what it seems to be when 
seen with the naked eye at the distance 
of most distinct vision (25 cm.). 

Measure the distance of the opening in 
the cardboard from the center of the lens 
and call it D . Then since the distance 
of the image (2)^) is 25 cm., the magnify- 
ing power of the lens can also be computed as the ratio 25/Z) . 

Since the lens formula is 1 = .-, and, for this virtual 

Do I>i f 




Scale 



Fig. 62 



±_ 



image, _Z), = — 25 cm., one gets the expression — — — . = - 



1^ 
25 



and the magnifying power is 



25 



= 1 + 



25 



1 

Do 25 /' 

Compute the 



OV f 

magnifying power of the lens also by means of this equa- 
tion, using the value of/ found in the first part of this ex- 



104 LABORATORY MANUAL 

periment. Record these three values of the magnifying 
power. 

Draw carefully a diagram to show the relative positions of 
the eyes, the lens, the opening in the cardboard, and the 
paper scale. 

If time permits, repeat the experiment with another lens 
of slightly different focal length. 

Problem. What is the magnifying power of a 3-inch 
lens used as a simple magnifier? 

EXPERIMENT 49 

TELESCOPE AND COMPOUND MICROSCOPE 

How may two convex lenses be arranged to act like a telescope ? 
How may two convex lenses be arranged to act like a compound 
microscope ? 

Two short focus lenses (f . 2.5-7.5 cm.). Cardboard screen and holder. 

Long focus lens (f. 25 cm.). Two lens holders. 

Optical bench. Cardboard screen with wire 
Electric or gas lamp. netting and holder. 

I. Astronomical Telescope. Find the focal length of each 
lens, as in Exp. 48. 

Mount a short focus lens near one end of the meter stick 
and set up a cardboard screen at such a distance beyond 
that its surface is seen distinctly when the eye is held close 
to the lens. On the other side of the screen mount the long 
focus lens at such a distance from the screen that it shows a 
sharp image of some distant object. Measure and record on 
a diagram the distance of the screen from each lens. With- 
out disturbing the lenses, remove the screen and look through 
the short focus lens, or eye-piece, and observe that the image 
formed by the other lens, or objective, can be distinctly seen. 



TELESCOPE AND COMPOUND MICROSCOPE 



105 



These two lenses thus arranged constitute the essential parts 
of a very crude astronomical telescope. Measure the dis- 
tance between the lenses and compare this distance with the 
sum of the focal lengths. 

To measure the magnifying power of the telescope, fasten 
on the opposite wall of the room a strip of white paper with 
a series of thick black lines drawn across it at 
regular intervals of about one inch. Be sure 
this paper scale is about on a level with the 
axis of the telescope and that the lenses are so 
adjusted as to give a sharp image. Then look 
through the telescope with one eye and at the 
same time look at the scale directly with the 
other eye. Adjust the telescope so that object 
and image appear about as shown in Fig. 63, 
and so that one mark of the image exactly 
coincides with one mark of the object. Count 
the number of spaces between two successive 
marks of the image. This gives the magnify- 
ing power of the telescope. Compare this value 
with the ratio of the focal length of the ob- 
jective to the focal length of the eye-piece. 

II. Compound Microscope. Measure the focal 
length of each of two short focus lenses. Set up 
the eye-piece lens and the cardboard screen just as in Part I. 
Place the other short focus lens, the objective, about 25 cm. be- 
yond the screen. Then place the screen (Exp. 46) with the 
aperture covered with wire netting, illuminated by some kind 
of lamp, at such a distance beyond the objective that a sharp 
picture of the wire netting will be formed on the translucent 
screen. 

Measure and record on a diagram the distances between 
the screen and lenses. 



Fig. 63 



106 LABORATORY MANUAL 

Take away the translucent screen and observe the image 
of the wire netting through the eye-piece. 

Make a simple diagram to show the relative positions of 
the eye, the two lenses, and the object. 

Problem. A telescope has an objective of 30 ft. focal 
length and an eye-piece of 1 in. focal length. What is its 
magnifying power ? 

EXPERIMENT 50 

DISPERSION OF LIGHT BY A PRISM 

How may white light be separated into the primary colors by a 

prism ? 

Triangular 60° prism. Gas flame or incandescent lamp filament. 

Black cardboard. Pins. 

Rnler. 

To show how a beam of light is refracted by a triangular 
prism, place a prism on a sheet of paper and draw a sharp 
line around its edge. Then set up two pins D and E about 

10 cm. apart and located as 
shown in Fig. 64. Now look 
with one eye into the face AC 
of the prism in such a way that 
the images of D and E seem to 
be in line. Lay a ruler on the 
paper so that its edge EG- and 
the images of D and E, all seem 
to be in the same line. Remove 
the prism and draw straight lines through D and E and F 
and Gr. Also draw the path of the ray in the prism HK. 
The broken line DHK shows how a ray of light is refracted 
by a prism. 




DISPERSION OF LIGHT BY A PRISM 107 

Hold the prism in direct sunlight so as to refract the rays 
of light upon some shaded part of the floor. Place between 
the sun and the prism a sheet of black cardboard which has 
a horizontal slit 2 or 3 mm. wide. What colors can be 
recognized now on the floor ? What color is refracted most, 
that is, tvhich color lies farthest from the refracting angle A 
of the prism? Which color is refracted least, that is, which 
lies nearest to the angle ? Compare the width of the slit with 
the width of the band of color or spectrum. 

In another sheet of black cardboard cut two slits 2 mm. 
in width and about 2 mm. apart. Keeping one slit covered, 
observe the spectrum and then note the effect in the middle 
of the spectrum when it is uncovered. The middle of the 
colored band is where the two spectra overlap. Does this 
show that certain colors of the spectrum may unite to produce 
white ? Now remove the cardboard screen with the slits and 
observe that only the edges of the band of light are colored 
and not the middle. Why ? 

Arrange a fish-tail gas flame so that the narrow edge is 
turned toward the eye. Holding the prism in front, of the 
right eye with the refracting angle toward the nose, observe 
this flame (or better an electric light filament) at a distance 
of 2 or 3 m. How must one turn in order to observe 
the image of the flame ? What color is the image ? What 
color lies farthest toward the right and which farthest to the 
left ? What are the intervening colors ? 

Make a careful sketch to show just how the prism was 
held and what colors were seen. 

Question. If one pastes a strip of white paper upon a 
black card and, holding it in the sunlight, examines it by 
looking through a prism, he will see that the edges of the 
paper give the spectrum colors. But if one examines in the 
same way strips of red and blue paper, he will see only the 
color which the paper reflects. Explain. 



APPENDIX 



I. Rules for Computation 
Area of triangle = base x altitude 

Circumference of circle = ttD 
Area of circle = ttR 2 
Surface of sphere = ^ttR 2 
4tt£ 3 



Volume of sphere 

Volume of prism 
Volume of cylinder 



area of base x altitude 



7T = 31 or 3.14 



II. Table of Equivalents 



1 centimeter = 0.394 inch 
1 kilometer = 0.621 mile 
1 kilogram = 2.20 pounds 
1 liter = 1.06 quarts 

1 cm. 3 water weighs 1 gram 



1 inch = 2.54 centimeters 
1 foot = 30.5 centimeters 
1 ounce = 28.4 grams 
1 pound = 454 grams 
1 cu. ft. water weighs 62.4 pounds 



Alcohol, 95 % 
Aluminum 
Brass . . . 
Coal, anthracite 
Copper . . 
Gasolene . . 
Glass (Flint) 
Glass (Crow^n) 
Gold . . . 
Ice .... 
Iron . . . 



III. Table of Densities 

(In grams per cubic centimeter) 

0.807 Lead 11.4 

2.65 Marble 2.5-2.8 

8.4-8.7 Mercury 13.6 

1.4-1.8 Platinum 21.5 

8.93 Silver 10.5 

0.68-0.72 Tin 7.3 

3.0-3.6 Sea Water 1.03 

2.5-2.7 Wood — Ebony ... 1.2 

19.3 Oak .... 0.7-0.9 

0.918 Pine .... 0.4-0.6 

7.1-7.9 Zinc . : 7.1 

109 



110 



APPENDIX 



IV. Density of Dry Air at Different Temperatures and 
Pressures (Grams per Liter) 









Pressure in 


Millimeters 






rp 




















710 


720 


730 


740 


750 


760 


770 


780 


o°c. 


1.208 


1.225 


1.242 


1.259 


1.276 


1.293 


1.310 


1.327 


2 


1.199 


1.216 


1.233 


1.250 


1.267 


1.284 


1.300 


1.317 


4 


1.190 


1.207 


1.224 


1.241 


1.258 


1.274 


1.291 


1.308 


6 


1.182 


1.199 


1.215 


1.232 


1.248 


1.265 


1.282 


1.298 


8 


1.173 


1.190 


1.207 


1.223 


1.240 


1.256 


1.273 


1.289 


10 


1.165 


1.182 


1.198 


1.214 


1.231 


1.247 


1.264 


1.280 


12 


1.157 


1.173 


1.190 


1.206 


1.222 


1.238 


1.255 


1.271 


14 


1.149 


1.165 


1.181 


1.197 


1.214 


1.230 


1.246 


1.262 


16 


- 1.141 


1.157 


1.173 


1.189 


1.205 


1.221 


1.237 


1.253 


18 


1.133 


1.149 


1.165 


1.181 


1.197 


1.213. 


1.229 


1.245 


20 


1.125 


1.141 


1.157 


1.173 


1.189 


1.205 


1.220 


1.236 


22 


1.118 


1.133 


1.149 


1.165 


1.181 


1.196 


1.212 


1.228 


24 


1.110 


1.126 


1.141 


1.157 


1.173 


1.188 


1.204 


1.220 


26 


1.103 


1.118 


1.134 


1.149 


1.165 


1.180 


1.196 


1.211 


28 


1.095 


1.111 


1.126 


1.142 


1.157 


1.173 


1.188 


1.203 


30 


1.088 


1.103 


1.119 


1.134 


1.149 


1.165 


1.180 


1.195 



V. Tensile Strength of Wires 

(Kilograms per square millimeter) 

Aluminum 17-20 

Brass 31-39 

Copper, hard drawn 40-46 

Copper, annealed 28-31 

German Silver 46 

Iron, hard drawn 54-62 

Iron, annealed about 46 

Steel, ordinary about 110 

Steel, piano ..,,,,,...,,,,... 186-233 



APPENDIX 



111 



VI. Coefficients of Linear Expansion of Solids 



Aluminum .... 0.0000231 
Brass ...... 0.0000189 

Copper 0.0000167 

Glass (soft) .... 0.0000085 



" Invar " (Nickel steel) 0.0000009 

Quartz (fused) . . . 0.0000005 

Steel 0.000011 

Zinc 0.000026 



VII. Specific Heats of Various Substances 



Aluminum . . . . . 0.22 

Brass 0.090 

Copper 0.094 

Iron 0.12 



Lead . . . . ... 0.031 

Mercury 0.033 

Tin 0.055 

Zinc 0.093 



VIII. Electromotive Forces of Cells 



Volts 

Daniel! cell 1.1 

Gravity cell • . .1.1 

Sal-ammoniac cell 1.5 



Volts 

Dry cell 1.5 

Lead storage cell . . . . . 2.0 
Edison storage cell , . . .1.2 



IX. Specific Resistance and Temperature Coefficient 
(From Timbie's " Elements of Electricity ") 



Material (Commercial) 


Specific Resistance 

Ohms per Mil-Foot 

at 20° C. 


Temperature 

Coefficient = 

Increase per degree C. 

Resistance at 0° C. 


Aluminum 




17.4 

10.4 

10.65 

90. 

64. 

114 to 275 

250 to 450 

283 

300 

294 


0.00435 


Copper, annealed . 






0.0042 


Copper, hard drawn . . 
Iron, annealed .... 




0.005 


Iron, E. B. B. (Roebling) 
German Silver .... 




0.0046 
0.00025 


Manganin 




0.00001 


la la (Boker) , soft . . 
la la (Boker), hard . . 
Advance (Driver-Harris) 




0.000005 

0.00001 

0.00000 



112 



APPENDIX 



X. Resistance of Annealed Copper Wire 



B. &S. 
Gauge 


Diameter in 
Millimeters 


Diameter in 
Mils 


Area in 
Circular Mils 


Ohms per 1000 
Ft. at 20° C. 


Feet per Lb., 

Double Cotton 

Covered 


10 


2.59 


101.9 


10,380. 


1.00 


30.9 


11 


2.31 


90.7 


8,234. 


1.26 


38.9 


12 


2.05 


80.8 


6,530. 


1.59 


48.8 


13 


1.83 


72.0 


5,178. 


2.00 


61.5 


14 


1.63 


64.1 


4,107. 


2.52 


77.4 


15 


1.45 


57.1 


3,257. 


3.18 


97.2 


16 


1.29 


50.8 


2,583. 


4.01 


122. 


17 


1.15 


45.3 


2,048. 


5.06 


153. 


18 


1.02 


40.3 


1,624. 


6.37 


192. 


19 


.90 


35.4 


1,288. 


8.04 


247. 


20 


.81 


32.0 


1,022. 


10.1 


298. 


21 


.72 


28.5 


810. 


12.8 


375. 


22 


.64 


25.3 


643. 


16.1 


472. 


23 


.57 


22.6 


509. 


20.3 


585. 


24 


.51 


20.1 


404. 


25.6 


730. 


25 


.46 


17.90 


320. 


32.3 


901. 


26 


.41 


15.94 


254. 


40.8 


1123. 


27 


.36 


14.20 


202. 


51.4 


1389. 


28 


.32 


12.64 


159.8 


64.8 


1695. 


29 


.29 


11.26 


126.7 


81.7 


2127. 


30 


.26 


10.02 


100.5 


103. 


2564. 


31 


.23 


8.93 


79.7 


130. 




32 


.20 


7.95 


63.2 


164. 




33 


.18 


7.08 


50.1 


207. 




34 


.16 


6.30 


39.7 


261. 




35 


.14 


5.61 


31.5 


328. 




36 


.13 


5.00 


25.0 


414. 





It will be noticed in the table above that #13 wire is about half the size 
of # 10 wire, and so has twice as much resistance. In the same way # 16 wire 
is half the size of # 13, and has double the resistance.] 



APPENDIX 



113 



XI. Natural Sines and Tangents 



Angle 


Sine 


Tangent 


Angle 


Sine 


Tangent 


Angle 


Sjne 


Tangent 





0.000 


0.000 


31 


0.515 


0.601 


62 


0.883 


1.881 


1 


0.017 


0.017 


32 


0.530 


0.625 


63 


0.891 


1.963 


2 


0.035 


0.035 


33 


0.545 


0.649 


64 


0.899 


2.050 


3 


0.052 


0.052 


34 


0.559 


0.675 


66 


0.906 


2.145 


4 


0.070 


0.070 


35 


0.574 


0.700 


66 


0.914 


2.246 


5 


0.087 


0.087 


36 


0.588 


0.727 


67 


0.921 


2.356 


6 


0.105 


0.105 


37 


0.602 


0.754 


68 


0.927 


2.475 


7 


0.122 


0.123 


38 


0.616 


0.781 


69 


0.934 


2.605 


8 


0.139 


0.141 


39 


0.629 


0.810 


70 


0.940 


2.747 


9 


0.156 


0.158 


40 


0.643 


0.839 


71 


0.946 


2.904 


10 


0.174 


0.176 


41 


0.656 


0.869 


72 


0.951 


3.078 


11 


0.191 


0.194 


42 


0.669 


0.900 


73 


0.956 


3.271 


12 


0.208 


0.213 


43 


0.682 


0.933 


74 


0.961 


3.487 


13 


0.225 


0.231 


44 


0.695 


0.966 


75 


0.966 


3.732 


14 


0.242 


0.249 


45 


0.707 


1.000 


76 


0.970 


4.011 


15 


0.259 


0.268 


46 


0.719 


1.036 


77 


0.974 


4.331 


16 


0.276 


0.287 


47 


0.731 


1.072 


78 


0.978 


4.705 


17 


0.292 


0.306 


48 


0.743 


1.111 


79 


0.982 


5.145 


18 


0.309 


0.325 


49 


0.755 


1.150 


80 


0.985 


5.671 


19 


0.326 


0.344 


50 


0.766 


1.192 


81 


0.988 


6.314 


20 


0.342 


0.364 


51 


0.777 


1.235 


82 


0.990 


7.115 


21 


0.358 


0.384 


52 


0.788 


1.280 


83 


0.993 


8.144 


22 


0.375 


0.404 


53 


0.799 


1.327 


84 


0.995 


9.514 


23 


0.391 


0.424 


54 


0.809 


1.376 


85 


0.996 


11.43 


24 


0.407 


0.445 


55 


0.819 


1.428 


86 


0.998 


14.30 


25 


0.423 


0.466 


56 


0.829 


1.483 


87 


0.999 


19.08 


26 


0.438 


0.488 


57 


0.839 


1.540 


88 


0.999 


28.64 


27 


0.454 


0.510 


58 


0.848 


1.600 


89 


1.000 


57.29 


28 


0.469 


0.532 


59 


0.857 


1.664 


90 


1.000 


Infinity 


29 


0.485 


0.554 


60 


0.866 


1.732 




- 




30 


0.500 


0.577 


61 


0.875 


1.804 









114 



APPENDIX 
XII. Four-Figure Logarithms 



N 





I 


2 


3 


4 


5 


6 


7 


8 


9 


1234 


5 


6789 


IO 
II 
12 
13 
14 

15 
16 

17 
18 
19 


0000 
0414 
0792 

1139 
1461 

1761 
2041 
2304 
2553 
2788 


0043 
0453 
0828 
ii73 
1492 

1790 
2068 
2330 
2577 
2810 


0086 
0492 
0864 
1206 
1523 

1818 
2095 
2355 
2601 

2833 


0128 
0531 
0899 
1239 
1553 

1847 
2122 
2380 
2625 
2856 


0170 
0569 

0934 
1271 

1584 

1875 
2148 
2405 
2648 
2878 


0212 
0607 
0969 
1303 
1614 

1903 

2175 
2430 
2672 
2900 


0253 
0645 
1004 
1335 
1644 

1931 
2201 

2455 
2695 
2923 


0294 
0682 
1038 
1367 
1673 

1959 

2227 
2480 
2718 
2945 


^334 
3719 
1072 

1399 
1703 

1987 
2253 
2504 
2742 
2967 


0374 
0755 
1 106 
1430 
1732 

2014 
2279 

2529 
2765 
2989 


4 8 12 17 
4 8 11 15 
3 7 10 14 
3 6 10 13 
3 6 9 12 

3 6 8 11 
3 5 8 11 
2 5 7 10 
2 5 7 9 

2 4 7 9 


21 
19 
17 
16 

15 

14 
13 
12 
12 
11 


25 29 33 37 
23 26 30 34 
21 24 28 31 
19 23 26 29 
18 21 24 27 

17 20 22 25 
16 18 21 24 
15 17 20 22 
14 16 19 21 
13 16 18 20 


20 
21 
22 

23 
24 

25 
26 

27 
28 
29 

30 
31 

32 

33 
34 

35 
36 
37 
38 
39 


3010 
3222 

3424 
3617 
3802 

3979 
4150 
4314 
4472 
4624 

477i 
4914 
5051 
5185 
5315 

544i 
5563 
5682 
5798 
59ii 


3032 
3243 
3444 
3636 
3820 

3997 
4166 
4330 
4487 
2639 

4786 
4928 
5065 
5198 
5328 

5453 
5575 
5694 
5809 
5922 


3054 
3263 
3464 
3655 
3838 

4014 
4183 
4346 
4502 
4654 

4800 
4942 
5079 
5211 
5340 

5465 
5587 
5705 
5821 

5933 


3075 
3284 
3483 
3674 
3856 

4031 

4200 
4362 
45i8 
4669 

4814 

4955 
5092 
5224 
5353 

5478 
5599 
5717 
5832 
5944 


3096 
3304 
3502 
3692 
3874 

4048 
4216 
4378 
4533 
4683 

4829 
4969 
5105 
5237 
5366 

5490 
5611 
5729 
5843 
5955 


3118 
3324 
3522 
3711 
3892 

4065 
4232 
4393 
4548 
4698 


3i39 
3345 
3541 
3729 
3909 

4082 

4249 
4409 

4564 
4713 


3160 
3365 
356o 
3747 
3927 

4099 
4265 
4425 
4579 
4728 


3181 
3385 
3579 
3766 

3945 

4116 
4281 
4440 
4594 
4742 


3201 
3404 
3598 
3784 
3962 

4i33 
4298 
4456 
4609 
4757 


2468 
2468 
2468 
2467 
2 4 5 7 

2 3 5 7 
2 3 5 7 
2356 
2356 
1346 


11 
10 

10 
9 
9 

9 

8 
8 
8 
7 


13 15 17 19 
12 14 16 18 
12 14 15 17 

11 13 15 17 
11 12 14 16 

10 12 14 15 

10 11 13 15 

9 11 13 14 

9 11 12 14 

9 10 12 13 


4843 
4983 
5ii9 
5250 
5378 

5502 
5623 
5740 
5855 
5966 


4857 
4997 
5132 
5263 
5391 

5514 
5635 
5752 
5866 
5977 


4871 
5011 
5145 
5276 

5403 

5527 
5647 
5763 
5877 
5988 


4886 
5024 
5159 
5289 
54i6 

5539 
5658 
5775 
5888 
5999 


4900 
5038 
5172 
5302 
5428 

555i 
5670 
5786 
5899 
6010 


13 4 6 
1346 
13 4 5 
13 4 5 
13 4 5 

1245 
1245 
1235 
1235 
1234 


7 
7 
7 
6 
6 

6 
6 

6 
6 

5 


9 10 11 13 
8 10 11 12 
8 9 11 12 
8 9 10 12 
8 9 10 11 

7 9 10 11 
7 8 10 11 
7 8 9 10 
7 8 9 10 
7 8 9 10 


40 
4i 
42 
43 

44 

45 
46 
47 
48 
49 


6021 
6128 
6232 
6335 
6435 

6532 
6628 
6721 
6812 
6902 


6031 
6138 
6243 

6345 
6444 

6542 
6637 
6730 
6821 
6911 


6042 
6149 
6253 
6355 
6454 

6551 
6646 
6739 
6830 
6920 


6053 
6160 
6263 

6365 
6464 

6561 
6656 
6749 
6839 
6928 


6064 
6170 
6274 
6375 
6474 

6571 
6665 
6758 
6848 
6937 


6075 
6180 
6284 
6385 
6484 

6580 
6675 
6767 
6857 
6946 


6085 
6191 
6294 
6395 
6493 

6590 
6684 
6776 
6866 
6955 


6096 
6201 
6304 
6405 
6503 

6599 
6693 
6785 
6875 
6964 


6107 
6212 
6314 
6415 
6513 

6609 
6702 

6794 
6884 
6972 


6117 
6222 

6325 
6425 
6522 

6618 
6712 
6803 

6893 
6981 


1234 
1234 
1234 
1234 
1234 

1234 
1234 
1234 
1234 
1234 


5 
5 
5 
5 
5 

5 

5 
5 
4 
4 


6 8 9 10 
6789 
6789 
6789 
6789 

6789 
6778 
5678 
5678 
5678 


50 
5i 
52 
53 
54 


6990 
7076 
7160 
7243 
7324 




6998 
7084 
7168 
7251 
7332 

I 


7007 
7093 
7177 
7259 
7340 

2 


7016 
7101 
7185 
7267 
7348 

3 


7024 
7110 
7193 

7275 
7356 

4 


7033 
7118 
7202 
7284 
7364 

5 


7042 
7126 
7210 
7292 
7372 

6 


7050 

7135 
7218 
7300 
738o 

7 


7059 
7143 
7226 
73o8 
7388 

8 


7067 
7152 
7235 
73i6 
7396 


1233 
1233 
1223 
1223 
1223 


4 

4 
4 
4 
4 


5678 
5678 
5677 
5667 
5667 


9 


12 3 4 


5 


6789 



APPENDIX 



115 









XII. FouR-FiGi 


[JRE 


Logarithms - 


— Continm 


3d 




N 





I 


2 


3 


4 


5 


6 


7 


8 


9 

7474 
755i 
7627 
7701 
7774 

7846 
7917 
7987 
8055 
8122 

8189 
8254 
8319 
8382 

8445 

8506 

8567 
8627 
8686 
8745 

8802 
8859 
8915 
8971 
9025 

9079 
9133 
9186 
9238 
9289 

9340 
9390 
9440 
9489 
9538 


1234 


5 


6789 


55 
56 
57 
58 
59 

60 
61 
62 
63 
64 

65 
66 

67 
68 
69 

70 

7i 
72 

73 
74 

75 
76 
77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 

92 

93 
94 

95 
96 
97 
98 
99 


7404 
7482 
7559 
7634 
7709 

7782 
7853 
7924 
7993 
8062 

8129 
8i95 
8261 

8325 
8388 

8451 
8513 
8573 
8633 
8692 

8751 
8808 
8865 
8921 
8976 

9031 
9085 
9138 
9191 
9243 

9294 
9345 
9395 
9445 
9494 

9542 
9590 
9638 
9685 
9731 

9777 
9823 
9868 
9912 
9956 




7412 
7490 
7566 
7642 
7716 

7789 
7860 

793i 
8000 
8069 

8136 
8202 
8267 
8331 
8395 

8457 
8519 
8579 
8639 
8698 

8756 
8814 
8871 
8927 
8982 

9036 
9090 

9143 
9196 
9248 

9299 
935o 
9400 
9450 
9499 

9547 
9595 
9643 
9689 
9736 

9782 
9827 
9872 
9917 
9961 

I 


7419 
7497 
7574 
7649 

7723 

7796 
7868 
7938 
8007 
8075 

8142 
8209 
8274 
8338 
8401 

8463 
8525 
8585 
8645 
8704 

8762 
8820 
8876 
8932 
8987 

9042 
9096 
9149 
9201 
9253 

9304 
9355 
9405 
9455 
9504 

9552 
9600 
9647 
9694 
9741 

9786 
9832 
9877 
9921 

9965 

2 


7427 
7505 
7582 
7657 
773i 

7803 
7875 
7945 
8014 
8082 

8i49 
8215 
8280 
8344 
8407 

8470 
853i 
8591 
8651 
8710 

8768 
8825 
8882 
8938 
8993 

9047 
9101 

9154 
9206 
9258 

9309 
9360 
9410 
9460 
9509 


7435 
7513 
7589 
7664 
7738 

7810 
7882 
7952 
8021 
8089 

8156 
8222 
8287 
8351 
8414 

8476 
8537 
8597 
8657 
8716 

8774 
8831 

8887 

8943 
8998 

9053 
9106 

9159 
9212 
9263 

9315 
9365 
9415 
9465 
9513 


7443 
7520 
7597 
7672 

7745 

7818 
7889 
7959 
8028 
8096 

8162 
8228 
8293 
8357 
8420 

8482 
8543 
8603 
8663 
8722 

8779 
8837 
8893 
8949 
9004 

9058 
9112 
9165 
9217 
9269 

9320 
9370 
9420 
9469 
95i8 


7451 
7528 
7604 
7679 
7752 

7825 
7896 

7966 

8035 
8102 

8169 

8235 

8299 

8363 
8426 

8488 

8549 
8609 
8669 
8727 

8785 

8842 
8899 
8954 

9009 

9063 
9117 
9170 

9222 

9274 
9325 

9375 
9425 
9474 
9523 


7459 
7536 
7612 
7686 
7760 

7832 
7903 
7973 
8041 
8109 

8176 
8241 
8306 
8370 
8432 

8494 
8555 
8615 
8675 
8733 

8791 

8848 
8904 
8960 

9015 

9069 
9122 

9175 
9227 

9279 

9330 
9380 
9430 
9479 
9528 


7466 

7543 
7619 
7694 
7767 

7839 
7910 
7980 
8048 
8116 

8182 
8248 
8312 
8376 
8439 

8500 
8561 
8621 
8681 
8739 

8797 
8854 
8910 
8965 
9020 

9074 
9128 
9180 
9232 
9284 

9335 
9385 
9435 
9484 
9533 


1223 
1223 
1223 
1 1 2 3 
1 1 2 3 


4 
4 
4 
4 
4 


5567 
5567 
5567 
4567 
4567 


1 1 2 3 
1 1 2 3 
1 1 2 3 
1 1 2 3 
1 1 2 3 

1 1 2 3 
1 1 2 3 
1 1 2 3 
1 1 .2 3 
1 1 2 2 


4 
4 
3 
3 
3 

3 
3 
3 
3 
3 


4566 
4566 
4566 
4 5 5 6 
4 5 5 6 

4 5 5 6 
4 5 5 6 
4 5 5 6 
4 4 5 6 
4 4 5 6 


1 1 2 2 
i 1 2 2 
1 1 2 2 
1 1 2 2 
1 1 2 2 

1 1 2 2 
1 1 2 2 

I 1 2 2 

II 22 
1 1 2 2 


3 
3 
3 
3 
3 

3 
3 
3 
3 
3 


4 4 5 6 
4 4 5 5 
4 4 5 5 
4 4 5 5 
4 4 5 5 

3 4 5 5 
3 4 5 5 
3 4 4 5 
3 4 4 5 
3 4 4 5 


1 1 2 2 
1 1 2 2 
1 1 2 2 
1 1 2 2 
1 1 2 2 

1 1 2 2 
1 1 2 2 
1 1 2 
1 1 2 
1 1 2 


3 
3 
3 
3 
3 

3 
3 
2 
2 

2 


3 4 4 5 
3 4 4 5 
3 4 4 5 
3 4 4 5 
3 4 4 5 

3 4 4 5 
3 4 4 5 
3 3 4 4 
3 3 4 4 
3 3 4 4 


9557 
9605 
9652 
9699 
9745 

9791 
9836 
9881 
9926 
9969 

3 


9562 
9609 
9657 
9703 
9750 

9795 
9841 
9886 
9930 
9974 

4 


9566 
9614 
9661 
9708 
9754 

9800 

9845 
9890 

9934 
9978 

5 


9571 
9619 
9666 
9713 
9759 

9805 
9850 
9894 
9939 
9983 

6 


9576 
9624 
9671 
9717 
9763 

9809 
9854 
9899 
9943 
9987 

7 


958i 
9628 

9675 
9722 
9768 

9814 
9859 
9903 
9948 
9991 

8 


9586 
9633 
9680 
9727 
9773 

9818 
9863 
9908 
9952 
9996 

9 


1 1 2 
1 1 2 
1 1 2 
1 1 2 
1 1 2 

1 1 2 
1 1 2 
i 1 2 
1 1 2 
1 1 2 


2 
2 
2 
2 
2 

2 
2 

2 
2 
2 


3 3 4 4 
3 3 4 4 
3 3 4 4 
3 3 4 4 
3 3 4 4 

3 3 4 4 

3 3 4 4 

,3344 

'3344 

3 3 3 4 


1234 


5 


6789 



116 



APPENDIX 



XIII. Antilogarithms 



Log 





I 


2 


3 


4 


5 


6 


7 


8 


9 


1234 


5 


6789 


.00 
.01 
.02 
.03 
.04 

•05 
.06 
.07 
.08 
.09 


1000 
1023 
1047 
1072 
1096 

1122 
1 148 

"75 

1202 
1230 


1002 
1026 
1050 
1074 
1099 

1125 
1151 
1178 
1205 
1233 


1005 
1028 
1052 
1076 
1 102 

1127 
1153 
1 180 
1208 
1236 


1007 
1030 

1054 
1079 
1 104 

1130 
1156 
"83 
1211 
1239 


1009 
1033 
1057 
1081 
1 107 

1132 

"59 
1186 
1213 
1242 


1012 
1035 
1059 
1084 
1 109 

"35 
1161 
1189 
1216 

1245 


1014 
1038 
1062 
1086 
1112 

1138 
1164 
1191 
1219 
1247 


1016 
1040 
1064 
1089 
1114 

1 140 
1167 
1 194 
1222 
1250 


1019 
1042 
1067 
1091 
1117 

1 143 
1 169 
1197 
1225 

1253 


1021 

1045 
1069 
1094 
1119 

1 146 
1172 
1199 

1227 
1256 


1 1 
1 1 
1 1 
1 1 
1 1 1 

1 1 1 
1 1 1 

O I I T 
O I I I 
O I I I 




1222 
1222 
1222 
1222 
2222 

2222 
2222 
2222 
2223 
2223 


.10 
.11 
.12 

• 13 
.14 

•15 
.16 

.17 
.18 
.19 


1259 
1288 
1318 
1349 
1380 

1413 
1445 
1479 
1514 
1549 


1262 
1291 
1321 
1352 
1384 
1416 
1449 
1483 
1517 
1552 


1265 
1294 
1324 
1355 
1387 

1419 
1452 
i486 
1521 
1556 


1268 
1297 
1327 
1358 
1390 

1422 

1455 
1489 

1524 
1560 


1271 
1300 
1330 
1361 
1393 
1426 
1459 
1493 
1528 
1563 


1274 
1303 
1334 
1365 
1396 

1429 
1462 
1496 
1531 
1567 


1276 
1306 
1337 
1368 
1400 

1432 
1466 
1500 
1535 
i57o 


1279 
1309 
1340 
1371 
1403 

1435 
1469 
1503 
1538 
1574 


1282 
1312 
1343 
1374 
1406 

1439 
1472 
1507 
1542 
1578 


1285 
1315 
1346 
1377 
1409 

1442 
1476 
1510 
1545 
1581 


O I I I 
O I I I 
O I I I 
O I I I 
O I I I 

O I I I 
O I I I 
O I I I 
O I I I 
O I I I 


2 
2 
2 
2 

2 
2 
2 
2 

2 


2223 
2223 
2223 
2233 
2233 

2233 
2233 
2233 
2233 
2 3 3 3 


.20 
.21 
.22 

.23 

.24 

.25 
.26 
.27 
.28 
.29 


1585 
1622 
1660 
1698 
1738 

1778 
1820 
1862 
1905 
1950 


1589 
1626 
1663 
1702 
1742 

1782 
1824 
1866 
1910 
1954 


1592 
1629 
1667 
1706 
1746 
1786 
1828 
1871 
1914 
1959 


1596 
1633 
1671 
1710 
I750 
1791 
1832 
1875 
1919 
1963 


1600 
1637 
1675 
1714 

1754 

1795 
1837 
1879 
1923 
1968 


1603 
1641 
1679 
1718 
1758 
1799 
1841 
1884 
1928 
1972 


1607 
1644 
1683 
1722 
1762 

1803 
1845 
1888 
1932 
1977 


1611 
1648 
1687 
1726 
1766 

1807 
1849 
1892 
1936 
1982 


1614 
1652 
1690 
1730 
1770 

1811 

1854 
1897 
1941 
1986 


1618 
1656 
1694 
1734 
1774 
1816 
1858 
1901 

1945 
1991 


O I I I 
O I I 2 
O I I 2 
O I I 2 
O I I 2 

O I I 2 
O I I 2 
O I I 2 
O I I 2 
O I I 2 


2 
2 
2 
2 
2 

2 
2 
2 
2 
2 


2 3 3 3 
2 3 3 3 
2 3 3 3 
2 3 3 4 
2 3 3 4 

2 3 3 4 

3 3 3 4 
3 3 3 4 
3 3 4 4 
3 3 4 4 


.30 
•31 
.32 
•33 
•34 

•35 
.36 
•37 
.38 
•39 


1995 
2042 
2089 
2138 
2188 

2239 
2291 
2344 
2399 
2455 


2000 
2046 
2094 
2143 
2193 

2244 
2296 
23S0 
2404 
2460 


2004 
2051 
2099 
2148 
2198 

2249 
2301 

2355 
2410 
2466 


2009 
2056 
2104 
2153 
2203 

2254 
2307 
2360 
2415 

2472 


2014 
2061 
2109 
2158 
2208 

2259 
2312 
2366 
2421 
2477 


2018 
2065 
2113 
2163 
2213 

2265 
2317 
2371 
2427 
2483 


2023 
2070 
2118 
2168 
2218 

2270 
2323 
2377 
2432 
2489 


2028 
2075 
2123 
2173 
2223 

2275 
2328 
2382 
2438 
2495 


2032 
2080 
2128 
2178 
2228 

2280 

2333 
2388 
2443 
2500 


2037 
2084 
2133 
2183 
2234 
2286 
2339 
2393 
2449 
2506 


O I I 2 
O I I 2 
O I I 2 

I I 2 

1 I 2 2 

I I 2 2 
I I 2 2 
I I 2 2 
I I 2 2 
I I 2 2 


2 
2 
2 
2 
3 

3 
3 
3 
3 
3 


3 3 4 4 
3 3 4 4 
3 3 4 4 
3 3 4 4 
3 4 4 5 

3 4 4 5 
3 4 4 5 
3 4 4 5 
3 4 4 5 

3 4 5 5 


.40 
.41 
.42 
•43 
.44 

•45 
.46 
•47 
.48 
•49 


2512 
2570 
2630 
2692 
2754 
2818 
2884 

2951 
3020 
3090 


2518 
2576 
2636 
2698 
2761 

2825 
2891 
2958 
3027 
3097 

I 


2523 
2582 
2642 
2704 
2767 

2831 
2897 
2965 
3034 
3I05 

2 


2529 
2588 
2649 
2710 
2773 
2838 
2904 
2972 

3041 
3112 


2535 
2594 
2655 
2716 
2780 

2844 
2911 
2979 
3048 
3"9 


2541 
2600 
2661 
2723 
2786 

2851 
2917 
2985 
3055 
3126 


2547 
2606 
2667 
2729 
2793 
2858 
2924 
2992 
3062 
3133 


2553 
2612 
2673 
2735 
2799 
2864 
2931 
2999 
3069 
3141 


2559 
2618 
2679 
2742 
2805 

2871 
2938 
3006 
3076 
3148 


2564 
2624 
2685 
2748 
2812 

2877 
2944 
3013 
3083 
3i55 


I I 2 2 
I I 2 2 
112 2 
I I 2 3 
I I 2 3 

I I 2 3 
I I 2 3 
I I 2 3 
I I 2 3 
I I 2 3 


3 
3 
3 
3 
3 

3 
3 
3 

4 
4 


4 4 5 5 
4 4 5 5 
4 4 5 
4 4 5 
4 4 5 6 

4 5 5 6 
4 5 5 
4 5 5 6 
4566 
4566 





3 


4 


5 


6 


7 


8 


9 


12 3 4 


5 


6789 



APPENDIX 



111 



XIII. Antilogakithms — Continued 



Log 

•50 





I 


2 


3 


4 


5 


6 


7 


8 


9 


I 


2 


3 


4 


5 


6 


789 


3162 


3170 


3177 


3184 


3192 


3199 


3206 


3214 


3221 


3228 


1 


I 


2 


3 


4 


4 


567 


.51 


3236 


3243 


3251 


3258 


3266 


3273 


3281 


3289 


3296 


3304 


1 


2 


2 


3 


4 


5 


567 


•52 


33ii 


3319 


3327 


3334 


3342 


3350 


3357 


3365 


3373 


338i 


1 


2 


2 


3 


4 


5 


567 


•53 


3388 


3396 


3404 


3412 


3420 


3428 


3436 


3443 


3451 


3459 


1 


2 


2 


3 


4 


5 


6 6 7 


•54 


3467 


3475 


3483 


3491 


3499 


3508 


35i6 


3524 


3532 


3540 


1 


2 


2 


3 


4 


5 


667 


•55 


3548 


3556 


3565 


3573 


358i 


3589 


3597 


3606 


3614 


3622 


1 


2 


2 


3 


4 


5 


677 


.56 


3631 


3639 


3648 3656 


3664 


3673 


3681 


3690 


3698 


3707 


1 


2 


3 


3 


4 


5 


678 


•57 


37i5 


3724 


3733 3741 


3750 


3758 


3767 


3776 


3784 


3793 


1 


2 


3 


3 


4 


5 


6 7 8 


•58 


3802 


3811381913828 


3837 


3846 


3855 


3864 


3873 


3882 


1 


2 


3 


4 


4 


5 


678 


•59 


3890 


389939083917 


3926 


3936 


3945 


3954 


3963 


3972 


1 


2 


3 


4 


5 


5 


6 7 8 


.60 


398i 


3990 


3999 


4009 


4018 


4027 


4036 


4046 


4055 


4064 


1 


2 


3 


4 


5 


6 


6 7 8 


.61 


4074 


4083 


4093 


4102 


4111 


4121 


4130 


4140 


4150 


4159 


1 


2 


3 


4 


5 


6 


789 


.62 


4169 


4178 


4188 


4198 


4207 


4217 


4227 


4236 


4246 


4256 


1 


2 


3 


4 


5 


6 


7 8 9 


.63 


4266 


4276 


4285 


4295 


4305 


4315 


4325 


4335 


4345 


4355 


1 


2 


3 


4 


5 


6 


7 8 9 


.64 


4365 


4375 


4385 


4395 


4406 


4416 


4426 


4436 


4446 


4457 


1 


2 


3 


4 


5 


6 


7 8 9 


.65 


4467 


4477 


4487 


4498 


4508 


4519 


4529 


4539 


4550 


456o 


1 


2 


3 


4 


5 


6 


7 8 9 


.66 


457i 


458i 


4592 


4603 


4613 


4624 


4634 


4645 


4656 


4667 


1 


2 


3 


4 


5 


6 


7 9 10 


.67 


4677 


4688 


4699 


4710 


4721 


4732 


4742 


4753 


4764 


4775 


1 


2 


3 


4 


5 


7 


8 9 10 


.68 


4786 


4797 


4808 


4819 


4831 


4842 


4853 


4864 


4875 


4887 


1 


2 


3 


4 


6 


7 


8 9 10 


.69 


4898 


4909 


4920 


4932 


4943 


4955 


4966 


4977 


4989 


5000 


1 


2 


3 


5 


6 


7 


8 9 10 


.70 


5012 


5023 


5035 


5047 


5058 


5070 


5082 


5093 


5105 


5ii7 


1 


2 


4 


5 


6 


7 


8 9 11 


.71 


5129 


5140 


5152 


5164 


5176 


5188 


5200 


5212 


5224 


5236 


1 


2 


4 


5 


6 


7 


8 10 11 


.72 


5248 


5260 


5272 


52845297 


5309 


5321 


5333 


5346 


5358 


1 


2 


4 


5 


6 


7 


9 10 11 


•73 


537o 


5383 


5395 


5408 5420 


5433 


5445 


5458 


5470 


5483 


1 


3 


4 


5 


6 


8 


9 10 11 


•74 


5495 


55o8 


5521 


5534 


5546 


5559 


5572 


5585 


5598 


5610 


1 


3 


4 


5 


6 


8 


9 10 12 


•75 


5623 


5636 5649 


5662 


5675 


5689 


5702 


5715 


5728 5741 


1 


3 


4 


5 


7 


8 


9 10 12 


.76 


5754 


5768!578i 


5794 


5808 


5821 


583458485861:5875 


1 


3 


4 


5 


7 


8 


9 11 12 


•77 


5888 


5902 59i6 


5929I5943 


5957 


5970J5984 5998 6012 


1 


3 


4 


5 


7 


8 


10 11 12 


.78 


6026 


6039 6053 '6067 6081 


6095 


610916124 


6138:6152 


1 


3 


4 


6 


7 


8 


10 11 13 


•79 


6166 


6180 6194 6209 6223 


6237 


6252 6266 


6281 6295 


1 


3 


4 


6 


7 


9 


10 11 13 


.80 


6310 


6324 6339 6353 6368 


6383 


6397 6412 


6427 6442 


1 


3 


4 


6 


7 


9 


10 12 13 


.81 


0457 


6471 6486 


6501 6516 


6531 


6546 6561 


6577 6592 


2 


3 


5 


6 


8 


9 


11 12 14 


.82 


6607 


6622 6637 


66536668 


6683 


6699 


6714 


6730 6745 


2 


3 


5 


6 


8 


9 


11 12 14 


.83 


6761 


6776 6792 


6808 6823 


6839 


6855 


6871 


6887 


6902 


2 


3 


5 


6 


8 


9 


11 13 14 


.84 


6918 


6934 


6950 


6966 


6982 


6998 


7015 


7031 


7047 


7063 


2 


3 


5 


6 


8 


10 


11 13 15 


.85 


7079 


7096 


7112 


7129 


7145 


7161 


7178 


7194 


7211 


7228 


2. 


3 


5 


7 


8 


10 


12 13 15 


.86 


7244 


7261 


7278 


7295 


73ii 


7328 


7345 


7362 


7379 


7396 


2 


3 


5 


7 


8 


10 


12 13 15 


.87 


7413 


7430 


7447 


7464 


7482 


7499 


75i6 


7534 


755i 


7568 


2 


3 


5 


7 


9 


10 


12 14 16 


.88 


7586 


7603 


7621 


7638 7656 


7674 


7691 


7709 


7727 


7745 


2 


4 


5* 


7 


9 


11 


12 14 16 


.89 


7762 


778o7798 


7816 


7834 


7852 


7870 


7889 


7907 


7925 


2 


4 


5 


7 


9 


11 


13 14 16 


.90 


7943 


7962 7980 


7998 


8017 


8035 


8054 


8072 


8091 8110 


2 


4 


6 


7 


9 


11 


13 15 17 


.91 


8128 


8147 8166 


8185 


8204 


8222 


8241 


8260 


82798299 


2 


4 


6 


S 


9 


11 


13 15 17 


.92 


8318 


8337 8356 


8375 


8395 


8414 


8433 


8453 


847218492 


2 


4 


6 


8 


10 


12 


14 15 17 


•93 


8511 


8531 8551 


S570 8590 


8610 


8630 


8650 


8670 8690 


2 


4 


6 


8 


10 


12 


14 16 18 


•94 


8710 


87308750 


87708790 


8810 


8831 


8851 


8872 8892 


2 


4 


6 


8 


10 


12 


14 16 18 


•95 


8913 


8933 8954 


89748995 


9016 


9036 


9057 


9078 9099 


2 


4 


6 


8 


10 


12 


15 17 19 


.96 


9120 


9141 9162 


9183 9204 


9226 


9247 


9268 


9290:9311 


2 


4 


6 


8 


11 


13 


15 17 19 


•97 


9333 


93549376 


9397 9419 


9441 


9462 


9484 


95069528 


2 


4 


7 


9 


11 


13 


15 17 20 


.98 


9550 


9572J9594 


9616 9638 


9661 


9683 


9705 


9727 975o 


2 


4 


7 


9 


11 


13 


16 18 20 


•99 


9772 



97959817 


9840 9863 


9886 


9908 


9931 


9954 9977 


2 


5 


7 


9 


11 


14 


16 18 20 


I 


2 


3 4 


5 


6 


7 


8 9 


I 


2 


3 


4 


5 


6 


789 



T 



HE following pages contain advertisements of a 
few of the Macmillan books on kindred subjects 



Practical Physics for Secondary Schools 

By N. HENRY BLACK of the Roxbury Latin School, 
Boston, and Professor HARVEY N. DAVIS of Harvard 
University. 

Cloth, i2mo, illustrated, 488 pages. List price, $1.25 

" In preparing this book," say the authors in the Preface, " we have tried to 
select only those topics which are of vital interest to young people, whether or 
not they intend to continue the study of physics in a college course. 

" Jn particular, we believe that the chief value of the informational side of 
such a course lies in its applications to the machinery of daily life. Everybody 
needs to know something about the working of electrical machinery, optical 
instruments, ships, automobiles, and all those labor-saving devices, such as 
vacuum cleaners, tireless cookers, pressure cookers, and electric irons, which 
are found in many American homes. We have, therefore, drawn as much of 
our illustrative material as possible from the common devices in modern life. 
We see no reason why this should detract in the least from the educational 
value of the study of physics, for one can learn to think straight just as well by 
thinking about an electrical generator, as by thinking about a Geissler tube. . . . 

" To understand any machine clearly, the student must have clearly in mind 
the fundamental principles involved. Therefore, although we have tried to 
begin each new topic, however short, with some concrete illustration familiar 
to young people, we have proceeded, as rapidly as seemed wise, to a deduction 
of the general principle. Then, to show how to make use of this principle, we 
have discussed other practical applications. We have tried to emphasize still 
further the value of principles, that is, generalizations, in science, by summariz- 
ing at the end of each chapter the principles discussed in that chapter. In 
these summaries we have aimed to make the phrasing brief and vivid so that 
it may be easily remembered and easily used." 

The new and noteworthy features of the book are the admirable 
selection of familiar material used to develop and apply the principles 
of physical science, the exceptionally clear and forceful exposition, 
showing the hand of the master teacher, the practical, interesting, 
thought-provoking problems, and the superior illustrations. 



THE MACMILLAN COMPANY 

64-66 Fifth Avenue 
Chicago New York City Dallas 

Boston Atlanta San Francisco 



Chemistry and its Relations to Daily Life 

By LOUIS KAHLENBERG and EDWIN B. HART 

Professors of Chemistry in the University of Wisconsin 

Cloth, i2mo, illustrated, 3Q3 pages. List price, $1.2$ 



If the contributions of chemical science to modern civilization 
were suddenly swept away, what a blank there would be ! If, on 
the other hand, every person were acquainted with the elements of 
chemistry and its bearing upon our daily life, what an uplift human 
efficiency would receive ! It is to further this latter end that this 
book has been prepared. Designed particularly for use by students 
of agriculture and home economics in secondary schools, its use will 
do much to increase the efficiency of the farm and the home. In 
the language of modern educational philosophy, it " functions in the 
life of the pupil.'" 

Useful facts rather than mere theory have been emphasized, 
although the theory has not been neglected. The practical char- 
acter of the work is indicated by the following selected chapter 
headings : 

IL The Composition and Uses of Water* 

IV* The Air, Nitrogen* Nitric Acid* and Ammonia* 

IX. Carbon and Its Compounds* 

XII* Paints* Oils* and Varnishes* 

XIII* Leather* Silk* Wool* Cotton* and Rubber* 

XV* Commercial Fertilizers* 

XVI* Farm Manure* 

XX* Milk and Its Products* 

XXL Poisons for Farm and Orchard Pests* 



THE MACMILLAN COMPANY 

64-66 FIFTH AVENUE 

BOSTON NEW YORK CITY DALLAS 

CHICAGO > ATLANTA SAN FRANCISCO 



Botany for Secondary Schools 

By L. H. BAILEY 

Of Cornell University 

Cloth, i2mo, illustrated, 460 pages. List price, $1.25 

It is not essential nor desirable that everybody should become a botanist, 
but it is inevitable that people shall be interested in the more human side 
of plant and animal life. We are interested in the evident things of natural 
history, and the greater our interest in such things, the wider is our horizon 
and the deeper our hold on life. 

The secondary school could not teach botanical science if it would ; lack of 
time and the immaturity of the pupils forbid it. But it can encourage a 
love of nature and an interest in plant study; indeed, it can originate these, 
and it does. Professor Bailey's Botany has been known to do it. 

In the revision of this book that has just been made, the effective simplicity 
of the nature teacher and the genuine sympathy of the nature lover are as 
successfully blended as they were in the former book. Bailey's Botany for 
Secondary Schools recognizes four or five general life principles : that no 
two natural things are alike ; that each individual has to make and main- 
tain its place through struggle with its fellows ; that " as the twig is bent 
the tree inclines " ; that " like produces like," and so on. From these 
simple laws and others like them Professor Bailey proceeds to unfold a 
wonderful story of plant individuals that have improved upon their race 
characteristics, of plant communities that have adopted manners from 
their neighbors, of features and characteristics that have been lost by 
plants because of changed conditions of life or surroundings. The story 
vibrates with interest. 

The book is, moreover, perfectly organized along the logical lines of 
approach to a scientific subject. Four general divisions of material insure 
its pedagogical success : 

Part I. — The Plant Itself; 

Part II. — The Plant in Its Relation to Environment and to Man; 

Part III. — Histology, or the Minute Structure of Plants ; 

PART IV. — The Kinds of Plants, including a Flora of 130 pages. 



THE MACMILLAN COMPANY 

Publishers 64-66 Fifth Avenue New York 

BOSTON CHICAGO ATLANTA DALLAS SAN FRANCISCO 



Shelter and Clothing : 

A TEXTBOOK OF THE HOUSEHOLD ARTS 

By HELEN KINNE, Professor of Household Arts Educa- 
tion, and ANNA M. COOLEY, Assistant Professor of House- 
hold Arts Education, Teachers College, Columbia University. 
Cloth, i2mo, illustrated, 37 J pages. $uo 

This book and the volume, Foods and Household Management, that follows 
it, make up a full course in domestic matters not confined to details of cooking 
and sewing. The books treat fully, but with careful balance, every phase of 
home-making. The authors hold that Harmony will be the keynote of the 
home in proportion as the makers of the home regard the plan, the sanitation, 
the decoration of the house itself, and as they exercise economy and wisdom in 
the provision of food and clothing. 

" Home Economics stands for the utilization of the resources of modern 
science to improve home life," and to this end homemakers should be con- 
versant with modern scientific thought on matters domestic. The best schemes 
of heating and lighting, modern arrangements for the disposal of waste, the 
sanitary efficiency of tinted walls, of bare floors, of furniture built on simple 
lines, these are some ways in which modern science instructs the intelligent 
homemaker. In the selection of textiles for clothing and domestic use, a 
housekeeper to be efficient must be able to distinguish between fabrics of dif- 
ferent fibers and to choose durable weaves, she must be able to detect adultera- 
tion and the deceptive " finishing " processes. In buying ready-made garments 
she must know how to protect herself and her family from the danger of gar- 
ments infected by diseased operators in sweatshops. The up-to-date book on 
home economy treats such topics and relates them to common experience. 

The plan of the book is flexible. Parts may be omitted or shifted to meet 
the necessity or the convenience of different schools. The chapter headings 
in some measure disclose the breadth, the variety, and the practicability of the 
book : 

The Home. — Its plan and construction ; heating, ventilating, lighting, 
water supply, and the disposal of waste ; decoration ; furnishing. Textiles. — 
Materials and how they are made. Garment-making. — Patterns ; cutting and 
making garments; embroidery. Dress. — History of costume; hygiene of 
clothing; economics of dress ; care and repair of clothing; millinery. 



THE MACMILLAN COMPANY 

64-66 Fifth Avenue 
Chicago New York City Dallas 

Boston Atlanta San Francisco 



. '-lis 



SEP 18 1913 



